Branquinho, Amílcar; Foulquié-Moreno, Ana; Fradi, Assil; Mañas, Manuel Matrix Jacobi biorthogonal polynomials via Riemann-Hilbert problem. (English) Zbl 07757742 Proc. Am. Math. Soc. 152, No. 1, 193-208 (2024). MSC: 33C45 42C05 39A36 39A12 34M50 15A16 PDFBibTeX XMLCite \textit{A. Branquinho} et al., Proc. Am. Math. Soc. 152, No. 1, 193--208 (2024; Zbl 07757742) Full Text: DOI arXiv
Forrester, Peter J. Rank 1 perturbations in random matrix theory – a review of exact results. (English) Zbl 07803560 Random Matrices Theory Appl. 12, No. 4, Article ID 2330001, 48 p. (2023). MSC: 15B52 15A18 33E17 34M55 34M56 42C05 60B20 60K35 PDFBibTeX XMLCite \textit{P. J. Forrester}, Random Matrices Theory Appl. 12, No. 4, Article ID 2330001, 48 p. (2023; Zbl 07803560) Full Text: DOI arXiv
Mu, Xinyu; Lyu, Shulin Hankel determinants for a Gaussian weight with Fisher-Hartwig singularities and generalized Painlevé IV equation. (English) Zbl 07763663 J. Phys. A, Math. Theor. 56, No. 47, Article ID 475201, 25 p. (2023). MSC: 15A15 15B52 60B20 33C45 33E17 34M55 PDFBibTeX XMLCite \textit{X. Mu} and \textit{S. Lyu}, J. Phys. A, Math. Theor. 56, No. 47, Article ID 475201, 25 p. (2023; Zbl 07763663) Full Text: DOI arXiv
Lastra, Alberto; Prisuelos-Arribas, Cruz Solutions of linear systems of moment differential equations via generalized matrix exponentials. (English) Zbl 1525.34128 J. Differ. Equations 372, 591-611 (2023). Reviewer: Mykola Grygorenko (Kyïv) MSC: 34M03 34M25 30D15 34A08 15A16 PDFBibTeX XMLCite \textit{A. Lastra} and \textit{C. Prisuelos-Arribas}, J. Differ. Equations 372, 591--611 (2023; Zbl 1525.34128) Full Text: DOI arXiv
Min, Chao; Chen, Yang Hankel determinant and orthogonal polynomials for a perturbed Gaussian weight: from finite \(n\) to large \(n\) asymptotics. (English) Zbl 1520.33006 J. Math. Phys. 64, No. 8, Article ID 083503, 20 p. (2023). MSC: 33C45 37J38 37J65 34M30 34M55 15B52 15A15 42C05 PDFBibTeX XMLCite \textit{C. Min} and \textit{Y. Chen}, J. Math. Phys. 64, No. 8, Article ID 083503, 20 p. (2023; Zbl 1520.33006) Full Text: DOI arXiv
Blower, Gordon; Doust, Ian Linear systems, Hankel products and the sinh-Gordon equation. (English) Zbl 1516.35369 J. Math. Anal. Appl. 525, No. 1, Article ID 127140, 24 p. (2023). Reviewer: Eugene Postnikov (Kursk) MSC: 35Q53 34M55 47B35 47A13 15B52 PDFBibTeX XMLCite \textit{G. Blower} and \textit{I. Doust}, J. Math. Anal. Appl. 525, No. 1, Article ID 127140, 24 p. (2023; Zbl 1516.35369) Full Text: DOI arXiv
Ghosal, Promit; Silva, Guilherme L. F. Universality for multiplicative statistics of Hermitian random matrices and the integro-differential Painlevé II equation. (English) Zbl 1515.37048 Commun. Math. Phys. 397, No. 3, 1237-1307 (2023). Reviewer: Anhui Gu (Chongqing) MSC: 37H10 15B52 60B20 34M55 37J65 PDFBibTeX XMLCite \textit{P. Ghosal} and \textit{G. L. F. Silva}, Commun. Math. Phys. 397, No. 3, 1237--1307 (2023; Zbl 1515.37048) Full Text: DOI arXiv
Riser, Roman; Kanzieper, Eugene Power spectrum of the circular unitary ensemble. (English) Zbl 1508.15030 Physica D 444, Article ID 133599, 22 p. (2023). Reviewer: Robert Conte (Gif-sur-Yvette) MSC: 15B52 15A18 15A15 33E17 34M55 PDFBibTeX XMLCite \textit{R. Riser} and \textit{E. Kanzieper}, Physica D 444, Article ID 133599, 22 p. (2023; Zbl 1508.15030) Full Text: DOI arXiv
Simon, Sergi Formal first integrals and higher variational equations. arXiv:2309.04449 Preprint, arXiv:2309.04449 [math.DS] (2023). MSC: 34A05 37C79 37J99 37J30 34M15 34C28 37C10 15A69 16W60 13F25 37N25 BibTeX Cite \textit{S. Simon}, ``Formal first integrals and higher variational equations'', Preprint, arXiv:2309.04449 [math.DS] (2023) Full Text: arXiv OA License
Livesay, Neal; Sage, Daniel S.; Nguyen, Bach Explicit constructions of connections on the projective line with a maximally ramified irregular singularity. arXiv:2303.06581 Preprint, arXiv:2303.06581 [math.AG] (2023). MSC: 15A83 34M50 14D05 34M35 BibTeX Cite \textit{N. Livesay} et al., ``Explicit constructions of connections on the projective line with a maximally ramified irregular singularity'', Preprint, arXiv:2303.06581 [math.AG] (2023) Full Text: arXiv OA License
Giorgadze, Grigory On the factorization and partial indices of piecewise constant matrix functions. (English) Zbl 1523.15011 Trans. A. Razmadze Math. Inst. 176, No. 3, 367-372 (2022). MSC: 15A23 34M03 34M35 PDFBibTeX XMLCite \textit{G. Giorgadze}, Trans. A. Razmadze Math. Inst. 176, No. 3, 367--372 (2022; Zbl 1523.15011) Full Text: Link
Yu, Jianduo; Li, Chuanzhong; Zhu, Mengkun; Chen, Yang Asymptotics for a singularly perturbed GUE, Painlevé III, double-confluent Heun equations, and small eigenvalues. (English) Zbl 1508.34121 J. Math. Phys. 63, No. 6, Article ID 063504, 25 p. (2022). MSC: 34M60 34M55 15B05 33C47 33C45 PDFBibTeX XMLCite \textit{J. Yu} et al., J. Math. Phys. 63, No. 6, Article ID 063504, 25 p. (2022; Zbl 1508.34121) Full Text: DOI
Khvoshchinskaya, L. A. Construction of the Fuchs differential equation with \(3\times 3\) residue-matrices and three singular points using logarithmization method. (English) Zbl 1517.34117 Lobachevskii J. Math. 43, No. 6, 1337-1344 (2022). Reviewer: Yoshitsugu Takei (Kyoto) MSC: 34M35 34M50 15A16 PDFBibTeX XMLCite \textit{L. A. Khvoshchinskaya}, Lobachevskii J. Math. 43, No. 6, 1337--1344 (2022; Zbl 1517.34117) Full Text: DOI
Bershtein, Mikhail; Gavrylenko, Pavlo; Grassi, Alba Quantum spectral problems and isomonodromic deformations. (English) Zbl 1507.81089 Commun. Math. Phys. 393, No. 1, 347-418 (2022). MSC: 81Q10 47A10 14D05 35Q15 34M50 34M55 35B44 15A63 PDFBibTeX XMLCite \textit{M. Bershtein} et al., Commun. Math. Phys. 393, No. 1, 347--418 (2022; Zbl 1507.81089) Full Text: DOI arXiv
Deaño, Alfredo; Simm, Nick Characteristic polynomials of complex random matrices and Painlevé transcendents. (English) Zbl 1514.15050 Int. Math. Res. Not. 2022, No. 1, 19000-19054 (2022). MSC: 15B52 35J65 34M40 34M55 60B20 PDFBibTeX XMLCite \textit{A. Deaño} and \textit{N. Simm}, Int. Math. Res. Not. 2022, No. 1, 19000--19054 (2022; Zbl 1514.15050) Full Text: DOI arXiv Link
Han, Pengju; Chen, Yang A degenerate Gaussian weight connected with Painlevé equations and Heun equations. (English) Zbl 07762525 Random Matrices Theory Appl. 10, No. 4, Article ID 2150034, 32 p. (2021). MSC: 33E17 33C45 33C47 34M55 15B52 60B20 PDFBibTeX XMLCite \textit{P. Han} and \textit{Y. Chen}, Random Matrices Theory Appl. 10, No. 4, Article ID 2150034, 32 p. (2021; Zbl 07762525) Full Text: DOI
Zhu, Mengkun; Wang, Dan; Chen, Yang Painlevé IV and the semi-classical Laguerre unitary ensembles with one jump discontinuities. (English) Zbl 1472.37062 Anal. Math. Phys. 11, No. 3, Paper No. 131, 19 p. (2021). MSC: 37J37 37J65 34M55 15B52 42C05 33E17 PDFBibTeX XMLCite \textit{M. Zhu} et al., Anal. Math. Phys. 11, No. 3, Paper No. 131, 19 p. (2021; Zbl 1472.37062) Full Text: DOI
Cafasso, Mattia; Claeys, Tom; Ruzza, Giulio Airy kernel determinant solutions to the KdV equation and integro-differential Painlevé equations. (English) Zbl 1477.37080 Commun. Math. Phys. 386, No. 2, 1107-1153 (2021). Reviewer: Andrei Pranevich (Grodno) MSC: 37K40 37J65 35Q53 34M55 45J05 15B52 60B20 PDFBibTeX XMLCite \textit{M. Cafasso} et al., Commun. Math. Phys. 386, No. 2, 1107--1153 (2021; Zbl 1477.37080) Full Text: DOI arXiv
Lyu, Shulin; Chen, Yang Gaussian unitary ensembles with two jump discontinuities, PDEs, and the coupled Painlevé II and IV systems. (English) Zbl 1472.82002 Stud. Appl. Math. 146, No. 1, 118-138 (2021). MSC: 82B05 15A15 15B52 33E17 33C45 42C05 34M55 PDFBibTeX XMLCite \textit{S. Lyu} and \textit{Y. Chen}, Stud. Appl. Math. 146, No. 1, 118--138 (2021; Zbl 1472.82002) Full Text: DOI arXiv
Zhu, Mengkun; Wang, Dan; Chen, Yang Painlevé IV, \(\sigma \)-form, and the deformed Hermite unitary ensembles. (English) Zbl 1461.42019 J. Math. Phys. 62, No. 3, Article ID 033508, 17 p. (2021). MSC: 42C05 15B52 33C45 34M55 PDFBibTeX XMLCite \textit{M. Zhu} et al., J. Math. Phys. 62, No. 3, Article ID 033508, 17 p. (2021; Zbl 1461.42019) Full Text: DOI arXiv
Branquinho, Amílcar; Foulquié Moreno, Ana; Mañas, Manuel Matrix biorthogonal polynomials: eigenvalue problems and non-Abelian discrete Painlevé equations. A Riemann-Hilbert problem perspective. (English) Zbl 1458.37073 J. Math. Anal. Appl. 494, No. 2, Article ID 124605, 36 p. (2021). Reviewer: Vladimir P. Kostov (Nice) MSC: 37K20 37K60 39A36 37J70 37J65 33C47 33E17 34M55 34M50 15A16 PDFBibTeX XMLCite \textit{A. Branquinho} et al., J. Math. Anal. Appl. 494, No. 2, Article ID 124605, 36 p. (2021; Zbl 1458.37073) Full Text: DOI arXiv
Harnad, John; Balogh, Ferenc Tau functions and their applications. (English) Zbl 1482.37001 Cambridge Monographs on Mathematical Physics. Cambridge: Cambridge University Press (ISBN 978-1-108-49268-3/hbk; 978-1-108-61090-2/ebook). xxvi, 521 p. (2021). Reviewer: Dimitar A. Kolev (Sofia) MSC: 37-02 37K10 37K15 37K20 37K25 37K30 37K35 37K40 35Q15 15B52 60B20 34M55 34M56 15A67 PDFBibTeX XMLCite \textit{J. Harnad} and \textit{F. Balogh}, Tau functions and their applications. Cambridge: Cambridge University Press (2021; Zbl 1482.37001) Full Text: DOI
Hu, Jie; Dzhamay, Anton; Chen, Yang Gap probabilities in the Laguerre unitary ensemble and discrete Painlevé equations. (English) Zbl 1519.39016 J. Phys. A, Math. Theor. 53, No. 35, Article ID 354003, 18 p. (2020). MSC: 39A36 39A12 15B52 34M55 33C45 PDFBibTeX XMLCite \textit{J. Hu} et al., J. Phys. A, Math. Theor. 53, No. 35, Article ID 354003, 18 p. (2020; Zbl 1519.39016) Full Text: DOI arXiv
Gharakhloo, Roozbeh; Its, Alexander A Riemann-Hilbert approach to asymptotic analysis of Toeplitz+Hankel determinants. (English) Zbl 1457.15008 SIGMA, Symmetry Integrability Geom. Methods Appl. 16, Paper 100, 47 p. (2020). Reviewer: Mohammed El Aïdi (Bogotá) MSC: 15A15 15B05 30E15 35Q15 34M50 47B35 PDFBibTeX XMLCite \textit{R. Gharakhloo} and \textit{A. Its}, SIGMA, Symmetry Integrability Geom. Methods Appl. 16, Paper 100, 47 p. (2020; Zbl 1457.15008) Full Text: DOI arXiv
Hinkkanen, Aimo; Ishizaki, Katsuya; Laine, Ilpo; Li, Kin Y. Complex oscillation of solutions of a third order ODE. (English) Zbl 1471.34167 Ann. Acad. Sci. Fenn., Math. 45, No. 1, 451-466 (2020). Reviewer: Risto Korhonen (Joensuu) MSC: 34M10 15A15 PDFBibTeX XMLCite \textit{A. Hinkkanen} et al., Ann. Acad. Sci. Fenn., Math. 45, No. 1, 451--466 (2020; Zbl 1471.34167) Full Text: DOI
Min, Chao; Chen, Yang Painlevé V, Painlevé XXXIV and the degenerate Laguerre unitary ensemble. (English) Zbl 1440.15038 Random Matrices Theory Appl. 9, No. 2, Article ID 2050016, 22 p. (2020). MSC: 15B52 33E17 34M55 37J65 PDFBibTeX XMLCite \textit{C. Min} and \textit{Y. Chen}, Random Matrices Theory Appl. 9, No. 2, Article ID 2050016, 22 p. (2020; Zbl 1440.15038) Full Text: DOI arXiv
Charlier, Christophe; Claeys, Tom Large gap asymptotics for Airy kernel determinants with discontinuities. (English) Zbl 1475.37014 Commun. Math. Phys. 375, No. 2, 1299-1339 (2020). Reviewer: Carlos Gabriel Pacheco (Ciudad de México) MSC: 37A50 15B52 15A15 60B20 60G55 34M50 PDFBibTeX XMLCite \textit{C. Charlier} and \textit{T. Claeys}, Commun. Math. Phys. 375, No. 2, 1299--1339 (2020; Zbl 1475.37014) Full Text: DOI arXiv
Dai, Dan; Xu, Shuai-Xia; Zhang, Lun Gaussian unitary ensembles with pole singularities near the soft edge and a system of coupled Painlevé XXXIV equations. (English) Zbl 1467.37057 Ann. Henri Poincaré 20, No. 10, 3313-3364 (2019). Reviewer: Yousuke Ohyama (Tokushima) MSC: 37J65 33E17 34M55 34M50 41A60 60B20 15B52 PDFBibTeX XMLCite \textit{D. Dai} et al., Ann. Henri Poincaré 20, No. 10, 3313--3364 (2019; Zbl 1467.37057) Full Text: DOI arXiv
Bailey, E. C.; Bettin, S.; Blower, G.; Conrey, J. B.; Prokhorov, A.; Rubinstein, M. O.; Snaith, N. C. Mixed moments of characteristic polynomials of random unitary matrices. (English) Zbl 1476.15054 J. Math. Phys. 60, No. 8, 083509, 26 p. (2019). MSC: 15B52 15A15 11M06 11M50 34M55 PDFBibTeX XMLCite \textit{E. C. Bailey} et al., J. Math. Phys. 60, No. 8, 083509, 26 p. (2019; Zbl 1476.15054) Full Text: DOI arXiv Link
Zhan, Longjun; Blower, Gordon; Chen, Yang; Zhu, Mengkun Center of mass distribution of the Jacobi unitary ensembles: Painlevé V, asymptotic expansions. (English) Zbl 1402.60012 J. Math. Phys. 59, No. 10, 103301, 27 p. (2018). MSC: 60B20 15B52 76W05 34M55 54E05 33E17 33C45 PDFBibTeX XMLCite \textit{L. Zhan} et al., J. Math. Phys. 59, No. 10, 103301, 27 p. (2018; Zbl 1402.60012) Full Text: DOI arXiv Link
Dumitrescu, Olivia; Mulase, Motohico Lectures on the topological recursion for Higgs bundles and quantum curves. (English) Zbl 1401.14001 Wentworth, Richard (ed.) et al., The geometry, topology and physics of moduli spaces of Higgs bundles. Based on minicourses from the program on “The geometry, topology and physics of moduli spaces of Higgs bundles”, IMS, Singapore, July 7 – August 29, 2014. Hackensack, NJ: World Scientific (ISBN 978-981-3229-08-2/hbk; 978-981-3229-10-5/ebook). Lecture Notes Series. Institute for Mathematical Sciences. National University of Singapore 36, 103-198 (2018). MSC: 14-01 81-01 81T45 14H70 14H81 14H15 14N35 15B52 14F10 14J26 33C05 33C10 33C15 34M60 53D37 PDFBibTeX XMLCite \textit{O. Dumitrescu} and \textit{M. Mulase}, Lect. Notes Ser., Inst. Math. Sci., Natl. Univ. Singap. 36, 103--198 (2018; Zbl 1401.14001) Full Text: DOI arXiv
Claeys, Tom; Doeraene, Antoine The generating function for the Airy point process and a system of coupled Painlevé II equations. (English) Zbl 1419.37063 Stud. Appl. Math. 140, No. 4, 403-437 (2018). Reviewer: Johanna Michor (Wien) MSC: 37K10 15B52 60B20 34M55 35Q55 60G55 PDFBibTeX XMLCite \textit{T. Claeys} and \textit{A. Doeraene}, Stud. Appl. Math. 140, No. 4, 403--437 (2018; Zbl 1419.37063) Full Text: DOI arXiv
Wu, Xiao-Bo; Xu, Shuai-Xia; Zhao, Yu-Qiu Gaussian unitary ensemble with boundary spectrum singularity and \(\sigma\)-form of the Painlevé II equation. (English) Zbl 1388.60033 Stud. Appl. Math. 140, No. 2, 221-251 (2018). MSC: 60B20 34M55 15B52 30E25 PDFBibTeX XMLCite \textit{X.-B. Wu} et al., Stud. Appl. Math. 140, No. 2, 221--251 (2018; Zbl 1388.60033) Full Text: DOI arXiv
Min, Chao; Chen, Yang Gap probability distribution of the Jacobi unitary ensemble: an elementary treatment, from finite \(n\) to double scaling. (English) Zbl 1388.60030 Stud. Appl. Math. 140, No. 2, 202-220 (2018). MSC: 60B20 34M55 15B52 PDFBibTeX XMLCite \textit{C. Min} and \textit{Y. Chen}, Stud. Appl. Math. 140, No. 2, 202--220 (2018; Zbl 1388.60030) Full Text: DOI arXiv
Fischer, Cyril; Náprstek, Jiří Remarks on inverse of matrix polynomials. (English) Zbl 1413.65202 Chleboun, J. (ed.) et al., Programs and algorithms of numerical mathematics 18. Proceedings of the 18th seminar (PANM), Janov nad Nisou, Czech Republic, June 19–24, 2016. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics. 24-29 (2017). Reviewer: Samuel D. Relton (Leeds) MSC: 65H10 15A15 15A18 30C10 34M03 PDFBibTeX XMLCite \textit{C. Fischer} and \textit{J. Náprstek}, in: Programs and algorithms of numerical mathematics 18. Proceedings of the 18th seminar (PANM), Janov nad Nisou, Czech Republic, June 19--24, 2016. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics. 24--29 (2017; Zbl 1413.65202) Full Text: DOI
Bothner, Thomas; Deift, Percy; Its, Alexander; Krasovsky, Igor On the asymptotic behavior of a log gas in the bulk scaling limit in the presence of a varying external potential. II. (English) Zbl 1382.82014 Bini, Dario A. (ed.) et al., Large truncated Toeplitz matrices, Toeplitz operators, and related topics. The Albrecht Böttcher anniversary volume. Basel: Birkhäuser/Springer (ISBN 978-3-319-49180-6/hbk; 978-3-319-49182-0/ebook). Operator Theory: Advances and Applications 259, 213-234 (2017). MSC: 82B23 47B35 34E05 34M50 15B05 PDFBibTeX XMLCite \textit{T. Bothner} et al., Oper. Theory: Adv. Appl. 259, 213--234 (2017; Zbl 1382.82014) Full Text: DOI arXiv
Lyu, Shulin; Chen, Yang Exceptional solutions to the Painlevé VI equation associated with the generalized Jacobi weight. (English) Zbl 1374.15015 Random Matrices Theory Appl. 6, No. 1, Article ID 1750003, 31 p. (2017). MSC: 15A15 34E05 34M55 15B52 PDFBibTeX XMLCite \textit{S. Lyu} and \textit{Y. Chen}, Random Matrices Theory Appl. 6, No. 1, Article ID 1750003, 31 p. (2017; Zbl 1374.15015) Full Text: DOI
Witte, N. S.; Forrester, P. J. Singular values of products of Ginibre random matrices. (English) Zbl 1370.37115 Stud. Appl. Math. 138, No. 2, 135-184 (2017). Reviewer: Dmitry Artamonov (Moskva) MSC: 37J35 34M55 15B52 33C10 60B20 34A34 PDFBibTeX XMLCite \textit{N. S. Witte} and \textit{P. J. Forrester}, Stud. Appl. Math. 138, No. 2, 135--184 (2017; Zbl 1370.37115) Full Text: DOI arXiv
Deift, Percy Some open problems in random matrix theory and the theory of integrable systems. II. (English) Zbl 1375.37160 SIGMA, Symmetry Integrability Geom. Methods Appl. 13, Paper 016, 23 p. (2017). Reviewer: Jonathan Eckhardt (Wien) MSC: 37K15 15B52 34M55 35Q53 60F05 60K35 62H25 82B44 35Q15 PDFBibTeX XMLCite \textit{P. Deift}, SIGMA, Symmetry Integrability Geom. Methods Appl. 13, Paper 016, 23 p. (2017; Zbl 1375.37160) Full Text: DOI arXiv
Atkin, Max R.; Claeys, Tom; Mezzadri, Francesco Random matrix ensembles with singularities and a hierarchy of Painlevé III equations. (English) Zbl 1404.60009 Int. Math. Res. Not. 2016, No. 8, 2320-2375 (2016). MSC: 60B20 34M55 15B52 PDFBibTeX XMLCite \textit{M. R. Atkin} et al., Int. Math. Res. Not. 2016, No. 8, 2320--2375 (2016; Zbl 1404.60009) Full Text: DOI arXiv
Chen, Min; Chen, Yang; Fan, Engui Perturbed Hankel determinant, correlation functions and Painlevé equations. (English) Zbl 1338.33020 J. Math. Phys. 57, No. 2, 023501, 31 p. (2016). MSC: 33C45 34M55 15A04 15A15 PDFBibTeX XMLCite \textit{M. Chen} et al., J. Math. Phys. 57, No. 2, 023501, 31 p. (2016; Zbl 1338.33020) Full Text: DOI arXiv
Basor, Estelle; Chen, Yang Perturbed Laguerre unitary ensembles, Hankel determinants, and information theory. (English) Zbl 1357.94046 Math. Methods Appl. Sci. 38, No. 18, 4840-4851 (2015). MSC: 94A15 34M55 15B52 33E17 PDFBibTeX XMLCite \textit{E. Basor} and \textit{Y. Chen}, Math. Methods Appl. Sci. 38, No. 18, 4840--4851 (2015; Zbl 1357.94046) Full Text: DOI
Claeys, T.; Krasovsky, I. Toeplitz determinants with merging singularities. (English) Zbl 1333.15018 Duke Math. J. 164, No. 15, 2897-2987 (2015). Reviewer: Andreas Arvanitoyeorgos (Patras) MSC: 15B05 15A15 33E17 35Q15 42C05 34M55 15B52 PDFBibTeX XMLCite \textit{T. Claeys} and \textit{I. Krasovsky}, Duke Math. J. 164, No. 15, 2897--2987 (2015; Zbl 1333.15018) Full Text: DOI arXiv Euclid
Bothner, Thomas; Its, Alexander Rudol’fovich Asymptotics of a cubic sine kernel determinant. (English) Zbl 1318.82015 St. Petersbg. Math. J. 26, No. 4, 515-565 (2015) and Algebra Anal. 26, No. 4, 2-91 (2014). MSC: 82B23 33E05 34E05 34M50 82C23 15B52 15A15 PDFBibTeX XMLCite \textit{T. Bothner} and \textit{A. R. Its}, St. Petersbg. Math. J. 26, No. 4, 515--565 (2015; Zbl 1318.82015) Full Text: DOI arXiv
Brightmore, L.; Mezzadri, F.; Mo, M. Y. A matrix model with a singular weight and Painlevé III. (English) Zbl 1316.15040 Commun. Math. Phys. 333, No. 3, 1317-1364 (2015). Reviewer: Ctirad Matonoha (Prague) MSC: 15B52 33E17 34M50 34M55 34M56 35F21 PDFBibTeX XMLCite \textit{L. Brightmore} et al., Commun. Math. Phys. 333, No. 3, 1317--1364 (2015; Zbl 1316.15040) Full Text: DOI arXiv
Balogh, F. Discrete matrix models for partial sums of conformal blocks associated to Painlevé transcendents. (English) Zbl 1309.33022 Nonlinearity 28, No. 1, 43-55 (2015). MSC: 33E17 15B52 34M55 81T40 PDFBibTeX XMLCite \textit{F. Balogh}, Nonlinearity 28, No. 1, 43--55 (2015; Zbl 1309.33022) Full Text: DOI arXiv
Assis, M.; Jacobsen, J. L.; Jensen, I.; Maillard, J.-M.; McCoy, B. M. Integrability versus non-integrability: hard hexagons and hard squares compared. (English) Zbl 1316.82008 J. Phys. A, Math. Theor. 47, No. 44, Article ID 445001, 53 p. (2014). Reviewer: Utkir A. Rozikov (Tashkent) MSC: 82B20 14H70 15A18 32G34 34M55 47E05 PDFBibTeX XMLCite \textit{M. Assis} et al., J. Phys. A, Math. Theor. 47, No. 44, Article ID 445001, 53 p. (2014; Zbl 1316.82008) Full Text: DOI arXiv
Cao, Man; Chen, Yang; Griffin, James Continuous and discrete Painlevé equations arising from the gap probability distribution of the finite \(n\) Gaussian unitary ensembles. (English) Zbl 1309.34144 J. Stat. Phys. 157, No. 2, 363-375 (2014). Reviewer: Dmitri Artamonov (Moskva) MSC: 34M55 15B52 PDFBibTeX XMLCite \textit{M. Cao} et al., J. Stat. Phys. 157, No. 2, 363--375 (2014; Zbl 1309.34144) Full Text: DOI arXiv
Bothner, Thomas; Its, Alexander Asymptotics of a Fredholm determinant corresponding to the first bulk critical universality class in random matrix models. (English) Zbl 1290.15004 Commun. Math. Phys. 328, No. 1, 155-202 (2014). MSC: 15A15 15A18 15B52 15B57 47A53 34M55 PDFBibTeX XMLCite \textit{T. Bothner} and \textit{A. Its}, Commun. Math. Phys. 328, No. 1, 155--202 (2014; Zbl 1290.15004) Full Text: DOI Link
Pierce, Virgil U. Continuum limits of Toda lattices for map enumeration. (English) Zbl 1290.05087 Dzhamay, Anton (ed.) et al., Algebraic and geometric aspects of integrable systems and random matrices. Proceedings of the AMS special session, Boston, MA, USA, January 6–7, 2012. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-8747-9/pbk; 978-1-4704-0991-3/ebook). Contemporary Mathematics 593, 317-345 (2013). MSC: 05C30 34M55 05A15 05A16 15B52 PDFBibTeX XMLCite \textit{V. U. Pierce}, Contemp. Math. 593, 317--345 (2013; Zbl 1290.05087) Full Text: DOI
Delvaux, Steven; Geudens, Dries; Zhang, Lun Universality and critical behaviour in the chiral two-matrix model. (English) Zbl 1280.81153 Nonlinearity 26, No. 8, 2231-2298 (2013). Reviewer: Stefan Weinzierl (Mainz) MSC: 81V35 81U99 15B52 81T80 34M50 41A60 60B20 PDFBibTeX XMLCite \textit{S. Delvaux} et al., Nonlinearity 26, No. 8, 2231--2298 (2013; Zbl 1280.81153) Full Text: DOI arXiv
Witte, N. S.; Bornemann, F.; Forrester, P. J. Joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles. (English) Zbl 1283.15114 Nonlinearity 26, No. 6, 1799-1822 (2013). Reviewer: Carlos Gabriel Pacheco (México D. F.) MSC: 15B52 60B20 15A18 15A42 34M55 PDFBibTeX XMLCite \textit{N. S. Witte} et al., Nonlinearity 26, No. 6, 1799--1822 (2013; Zbl 1283.15114) Full Text: DOI arXiv
Ivanov, Dmitri A.; Abanov, Alexander G.; Cheianov, Vadim V. Counting free fermions on a line: a Fisher-Hartwig asymptotic expansion for the Toeplitz determinant in the double-scaling limit. (English) Zbl 1321.82015 J. Phys. A, Math. Theor. 46, No. 8, Article ID 085003, 13 p. (2013). MSC: 82B20 15A15 30E25 33E17 34M55 34M50 PDFBibTeX XMLCite \textit{D. A. Ivanov} et al., J. Phys. A, Math. Theor. 46, No. 8, Article ID 085003, 13 p. (2013; Zbl 1321.82015) Full Text: DOI arXiv
Akemann, Gernot; Atkin, Max R. Higher order analogues of Tracy-Widom distributions via the Lax method. (English) Zbl 1257.82056 J. Phys. A, Math. Theor. 46, No. 1, Article ID 015202, 19p. (2013). MSC: 82B44 15B52 15B57 15A18 34M55 37K35 37M10 PDFBibTeX XMLCite \textit{G. Akemann} and \textit{M. R. Atkin}, J. Phys. A, Math. Theor. 46, No. 1, Article ID 015202, 19p. (2013; Zbl 1257.82056) Full Text: DOI arXiv
Deschout, K.; Kuijlaars, A. B. J. Critical behavior in Angelesco ensembles. (English) Zbl 1278.15039 J. Math. Phys. 53, No. 12, 123523, 21 p. (2012). MSC: 15B52 42C05 60G55 34M60 34L20 82D37 PDFBibTeX XMLCite \textit{K. Deschout} and \textit{A. B. J. Kuijlaars}, J. Math. Phys. 53, No. 12, 123523, 21 p. (2012; Zbl 1278.15039) Full Text: DOI arXiv Link
Aref, H.; Beelen, P.; Brøns, M. Bilinear relative equilibria of identical point vortices. (English) Zbl 1254.76041 J. Nonlinear Sci. 22, No. 5, 849-885 (2012). MSC: 76B47 34M99 34B24 15A15 PDFBibTeX XMLCite \textit{H. Aref} et al., J. Nonlinear Sci. 22, No. 5, 849--885 (2012; Zbl 1254.76041) Full Text: DOI
Basor, Estelle; Chen, Yang; Mekareeya, Noppadol The Hilbert series of \(\mathcal{N}=1\) \(SO(N_c)\) and \(Sp(N_c)\) SQCD, Painlevé VI and integrable systems. (English) Zbl 1246.81419 Nucl. Phys., B 860, No. 3, 421-463 (2012). MSC: 81V05 81T60 47B35 15B52 81R12 34M55 14D21 PDFBibTeX XMLCite \textit{E. Basor} et al., Nucl. Phys., B 860, No. 3, 421--463 (2012; Zbl 1246.81419) Full Text: DOI arXiv
Forrester, Peter J.; Rains, Eric M. A Fuchsian matrix differential equation for Selberg correlation integrals. (English) Zbl 1245.82030 Commun. Math. Phys. 309, No. 3, 771-792 (2012). Reviewer: Vladimir Mityushev (Kraków) MSC: 82B44 15B52 34M35 PDFBibTeX XMLCite \textit{P. J. Forrester} and \textit{E. M. Rains}, Commun. Math. Phys. 309, No. 3, 771--792 (2012; Zbl 1245.82030) Full Text: DOI arXiv Link
Verdier, Olivier Reduction and Normal Forms of Matrix Pencils. arXiv:1205.1138 Preprint, arXiv:1205.1138 [math.NA] (2012). MSC: 15A03 15A21 15A22 47A50 34M03 BibTeX Cite \textit{O. Verdier}, ``Reduction and Normal Forms of Matrix Pencils'', Preprint, arXiv:1205.1138 [math.NA] (2012) Full Text: arXiv OA License
Claeys, T.; Its, A.; Krasovsky, I. Emergence of a singularity for Toeplitz determinants and Painlevé V. (English) Zbl 1298.47039 Duke Math. J. 160, No. 2, 207-262 (2011). Reviewer: Edgar Pereira (Natal) MSC: 47B35 34M55 15A15 34M50 82B20 15B52 PDFBibTeX XMLCite \textit{T. Claeys} et al., Duke Math. J. 160, No. 2, 207--262 (2011; Zbl 1298.47039) Full Text: DOI arXiv
Its, Alexander R. Asymptotic analysis of the Toeplitz and Hankel determinants via the Riemann-Hilbert method. (English) Zbl 1238.47020 Bhatia, Rajendra (ed.) et al., Proceedings of the international congress of mathematicians (ICM 2010), Hyderabad, India, August 19–27, 2010. Vol. III: Invited lectures. Hackensack, NJ: World Scientific; New Delhi: Hindustan Book Agency (ISBN 978-981-4324-33-5/hbk; 978-81-85931-08-3/hbk; 978-981-4324-30-4/set; 978-981-4324-35-9/ebook). 1395-1410 (2011). Reviewer: Alexei Yu. Karlovich (Lisboa) MSC: 47B35 15B52 35Q15 34M55 PDFBibTeX XMLCite \textit{A. R. Its}, in: Proceedings of the international congress of mathematicians (ICM 2010), Hyderabad, India, August 19--27, 2010. Vol. III: Invited lectures. Hackensack, NJ: World Scientific; New Delhi: Hindustan Book Agency. 1395--1410 (2011; Zbl 1238.47020) Full Text: Link
Its, Alexander Discrete Painlevé equations and orthogonal polynomials. (English) Zbl 1229.39011 Levi, Decio (ed.) et al., Symmetries and integrability of difference equations. Based upon lectures delivered during the summer school, Montreal, Canada, June 8–21, 2008. Cambridge: Cambridge University Press (ISBN 978-0-521-13658-7/pbk). London Mathematical Society Lecture Note Series 381, 139-159 (2011). MSC: 39A12 34M55 15B52 42C05 PDFBibTeX XMLCite \textit{A. Its}, Lond. Math. Soc. Lect. Note Ser. 381, 139--159 (2011; Zbl 1229.39011)
Ludkowski, S. V.; Sprössig, W. Spectral theory of super-differential operators of quaternion and octonion variables. (English) Zbl 1238.47028 Adv. Appl. Clifford Algebr. 21, No. 1, 165-191 (2011). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 47E05 47B07 30G35 15B33 34M99 PDFBibTeX XMLCite \textit{S. V. Ludkowski} and \textit{W. Sprössig}, Adv. Appl. Clifford Algebr. 21, No. 1, 165--191 (2011; Zbl 1238.47028) Full Text: DOI
Ercolani, N. M. Caustics, counting maps and semi-classical asymptotics. (English) Zbl 1218.15017 Nonlinearity 24, No. 2, 481-526 (2011). Reviewer: Andrei A. Kapaev (Trieste) MSC: 15B52 05A15 05C30 37K10 60B20 34M55 PDFBibTeX XMLCite \textit{N. M. Ercolani}, Nonlinearity 24, No. 2, 481--526 (2011; Zbl 1218.15017) Full Text: DOI arXiv
Blower, Gordon On linear systems and \(\tau\) functions associated with Lamé’s equation and Painlevé’s equation VI. (English) Zbl 1218.47021 J. Math. Anal. Appl. 376, No. 1, 294-316 (2011). Reviewer: Hengyou Lan (Zigong) MSC: 47A48 37K10 15B52 60G55 34M55 35C05 PDFBibTeX XMLCite \textit{G. Blower}, J. Math. Anal. Appl. 376, No. 1, 294--316 (2011; Zbl 1218.47021) Full Text: DOI arXiv Link
Kostov, Vladimir P. Additive Deligne-Simpson problem for non-Fuchsian systems. (English) Zbl 1246.15018 Funkc. Ekvacioj, Ser. Int. 53, No. 3, 395-410 (2010). Reviewer: Michael Bogner (Mainz) MSC: 15A24 34M50 34M35 PDFBibTeX XMLCite \textit{V. P. Kostov}, Funkc. Ekvacioj, Ser. Int. 53, No. 3, 395--410 (2010; Zbl 1246.15018) Full Text: DOI
Middeke, Johannes Conversion between Hermite and Popov normal forms using an FGLM-like approach. (English) Zbl 1220.15014 Albanian J. Math. 4, No. 4, 181-193 (2010). MSC: 15A21 16S36 34M35 PDFBibTeX XMLCite \textit{J. Middeke}, Albanian J. Math. 4, No. 4, 181--193 (2010; Zbl 1220.15014)
Dueñez, E.; Huynh, D. K.; Keating, J. P.; Miller, S. J.; Snaith, N. C. The lowest eigenvalue of Jacobi random matrix ensembles and Painlevé VI. (English) Zbl 1206.34113 J. Phys. A, Math. Theor. 43, No. 40, Article ID 405204, 27 p. (2010). MSC: 34M55 60B20 15A18 15B52 33C45 82B44 PDFBibTeX XMLCite \textit{E. Dueñez} et al., J. Phys. A, Math. Theor. 43, No. 40, Article ID 405204, 27 p. (2010; Zbl 1206.34113) Full Text: DOI arXiv
Claeys, Tom; Krasovsky, Igor; Its, Alexander Higher-order analogues of the Tracy-Widom distribution and the Painlevé II hierarchy. (English) Zbl 1198.34191 Commun. Pure Appl. Math. 63, No. 3, 362-412 (2010). Reviewer: Andrei A. Kapaev (Trieste) MSC: 34M55 34M50 15B52 33E17 PDFBibTeX XMLCite \textit{T. Claeys} et al., Commun. Pure Appl. Math. 63, No. 3, 362--412 (2010; Zbl 1198.34191) Full Text: DOI arXiv
Dzhamay, Anton Factorizations of rational matrix functions with application to discrete isomonodromic transformations and difference Painlevé equations. (English) Zbl 1181.15016 J. Phys. A, Math. Theor. 42, No. 45, Article ID 454008, 10 p. (2009). Reviewer: Ondřej Došlý (Brno) MSC: 15A23 39A10 37K20 39A12 34M55 15A54 PDFBibTeX XMLCite \textit{A. Dzhamay}, J. Phys. A, Math. Theor. 42, No. 45, Article ID 454008, 10 p. (2009; Zbl 1181.15016) Full Text: DOI arXiv
Its, A. R.; Kuijlaars, A. B. J.; Östensson, J. Asymptotics for a special solution of the thirty fourth Painlevé equation. (English) Zbl 1177.15038 Nonlinearity 22, No. 7, 1523-1558 (2009). Reviewer: Benoit Collins (Ottawa) MSC: 15B52 15A18 34M55 PDFBibTeX XMLCite \textit{A. R. Its} et al., Nonlinearity 22, No. 7, 1523--1558 (2009; Zbl 1177.15038) Full Text: DOI arXiv Link
Bertola, M. Moment determinants as isomonodromic tau functions. (English) Zbl 1198.05150 Nonlinearity 22, No. 1, 29-50 (2009). MSC: 05E99 15A15 34M55 47B35 PDFBibTeX XMLCite \textit{M. Bertola}, Nonlinearity 22, No. 1, 29--50 (2009; Zbl 1198.05150) Full Text: DOI arXiv
Deift, Percy Some open problems in random matrix theory and the theory of integrable systems. (English) Zbl 1147.15305 Baik, Jinho (ed.) et al., Integrable systems and random matrices. In honor of Percy Deift. Conference on integrable systems, random matrices, and applications in honor of Percy Deift’s 60th birthday, New York, NY, USA, May 22–26, 2006. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4240-9/pbk). Contemporary Mathematics 458, 419-430 (2008). MSC: 15B52 35Q15 37K15 34M55 35Q53 35Q55 62H25 60F05 PDFBibTeX XMLCite \textit{P. Deift}, Contemp. Math. 458, 419--430 (2008; Zbl 1147.15305) Full Text: arXiv
Claeys, Tom; Kuijlaars, Arno B. J. Universality in unitary random matrix ensembles when the soft edge meets the hard edge. (English) Zbl 1147.15303 Baik, Jinho (ed.) et al., Integrable systems and random matrices. In honor of Percy Deift. Conference on integrable systems, random matrices, and applications in honor of Percy Deift’s 60th birthday, New York, NY, USA, May 22–26, 2006. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4240-9/pbk). Contemporary Mathematics 458, 265-279 (2008). MSC: 15B52 34M55 35Q15 PDFBibTeX XMLCite \textit{T. Claeys} and \textit{A. B. J. Kuijlaars}, Contemp. Math. 458, 265--279 (2008; Zbl 1147.15303) Full Text: arXiv
Its, A.; Krasovsky, I. Hankel determinant and orthogonal polynomials for the Gaussian weight with a jump. (English) Zbl 1163.15027 Baik, Jinho (ed.) et al., Integrable systems and random matrices. In honor of Percy Deift. Conference on integrable systems, random matrices, and applications in honor of Percy Deift’s 60th birthday, New York, NY, USA, May 22–26, 2006. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4240-9/pbk). Contemporary Mathematics 458, 215-247 (2008). Reviewer: Alexei Yu. Karlovich (Lisboa) MSC: 15B52 47B35 34E05 34M50 42C05 15A15 PDFBibTeX XMLCite \textit{A. Its} and \textit{I. Krasovsky}, Contemp. Math. 458, 215--247 (2008; Zbl 1163.15027) Full Text: arXiv
Baik, Jinho; Buckingham, Robert; DiFranco, Jeffery Asymptotics of Tracy-Widom distributions and the total integral of a Painlevé II function. (English) Zbl 1221.33032 Commun. Math. Phys. 280, No. 2, 463-497 (2008). Reviewer: Andrei A. Kapaev (Trieste) MSC: 33E17 34M55 47B35 15B52 PDFBibTeX XMLCite \textit{J. Baik} et al., Commun. Math. Phys. 280, No. 2, 463--497 (2008; Zbl 1221.33032) Full Text: DOI arXiv
Liu, Yiguang; You, Zhisheng; Cao, Liping A recurrent neural network computing the largest imaginary or real part of eigenvalues of real matrices. (English) Zbl 1135.15006 Comput. Math. Appl. 53, No. 1, 41-53 (2007). Reviewer: A. Arvanitoyeorgos (Rion) MSC: 15A18 34M30 68T05 92B20 65F15 PDFBibTeX XMLCite \textit{Y. Liu} et al., Comput. Math. Appl. 53, No. 1, 41--53 (2007; Zbl 1135.15006) Full Text: DOI
Forrester, Peter J. Evenness symmetry and inter-relationships between gap probabilities in random matrix theory. (English) Zbl 1130.82311 Forum Math. 18, No. 5, 711-743 (2006). MSC: 82B41 15B52 34M55 33C90 60A10 PDFBibTeX XMLCite \textit{P. J. Forrester}, Forum Math. 18, No. 5, 711--743 (2006; Zbl 1130.82311) Full Text: DOI
Desrosiers, Patrick; Forrester, Peter J. Relationships between \(\tau\)-functions and Fredholm determinant expressions for gap probabilities in random matrix theory. (English) Zbl 1116.15020 Nonlinearity 19, No. 7, 1643-1656 (2006). Reviewer: Václav Burjan (Praha) MSC: 15B52 15A90 34M55 45B05 60A10 82C31 PDFBibTeX XMLCite \textit{P. Desrosiers} and \textit{P. J. Forrester}, Nonlinearity 19, No. 7, 1643--1656 (2006; Zbl 1116.15020) Full Text: DOI arXiv
Chen, Yang; Feigin, M. V. Painlevé IV and degenerate Gaussian unitary ensembles. (English) Zbl 1108.15023 J. Phys. A, Math. Gen. 39, No. 40, 12381-12393 (2006). MSC: 15B52 81T30 82C44 34M55 PDFBibTeX XMLCite \textit{Y. Chen} and \textit{M. V. Feigin}, J. Phys. A, Math. Gen. 39, No. 40, 12381--12393 (2006; Zbl 1108.15023) Full Text: DOI arXiv Link
Forrester, P. J.; Witte, N. S. Random matrix theory and the sixth Painlevé equation. (English) Zbl 1119.34070 J. Phys. A, Math. Gen. 39, No. 39, 12211-12233 (2006). Reviewer: Andrei A. Kapaev (St. Petersburg) MSC: 34M55 37F10 33C45 15B51 PDFBibTeX XMLCite \textit{P. J. Forrester} and \textit{N. S. Witte}, J. Phys. A, Math. Gen. 39, No. 39, 12211--12233 (2006; Zbl 1119.34070) Full Text: DOI arXiv
Forrester, P. J.; Witte, N. S. Boundary conditions associated with the Painlevé III’ and V evaluations of some random matrix averages. (English) Zbl 1098.15017 J. Phys. A, Math. Gen. 39, No. 28, 8983-8995 (2006). Reviewer: Václav Burjan (Praha) MSC: 15B52 34M55 33C15 11M26 PDFBibTeX XMLCite \textit{P. J. Forrester} and \textit{N. S. Witte}, J. Phys. A, Math. Gen. 39, No. 28, 8983--8995 (2006; Zbl 1098.15017) Full Text: DOI arXiv
Eynard, B.; Kokotov, A.; Korotkin, D. \(1/N^{2}\) correction to free energy in Hermitian two-matrix model. (English) Zbl 1086.15023 Lett. Math. Phys. 71, No. 3, 199-207 (2005). Reviewer: Václav Burjan (Praha) MSC: 15B52 34M55 PDFBibTeX XMLCite \textit{B. Eynard} et al., Lett. Math. Phys. 71, No. 3, 199--207 (2005; Zbl 1086.15023) Full Text: DOI arXiv
Martins, Fernando; Pereira, Edgar; Vitória, José Block compound matrices and differential matrix equations. (English) Zbl 1086.15012 Far East J. Appl. Math. 17, No. 2, 221-242 (2004). Reviewer: Mihail M. Konstantinov (Sofia) MSC: 15A24 15A18 34A30 34M99 PDFBibTeX XMLCite \textit{F. Martins} et al., Far East J. Appl. Math. 17, No. 2, 221--242 (2004; Zbl 1086.15012)
Witte, N. S. Gap probabilities for double intervals in Hermitian random matrix ensembles as \({\tau}\)-functions – spectrum singularity case. (English) Zbl 1089.15023 Lett. Math. Phys. 68, No. 3, 139-149 (2004). Reviewer: Takayuki Nôno (Hiroshima) MSC: 15B52 33E17 34M55 82C22 37K35 PDFBibTeX XMLCite \textit{N. S. Witte}, Lett. Math. Phys. 68, No. 3, 139--149 (2004; Zbl 1089.15023) Full Text: DOI arXiv
Forrester, P. J.; Witte, N. S. Application of the \(\tau\)-function theory of Painlevé equations to random matrices: \(\text{P}_{\text{VI}}\), the JUE, CyUE, cJUE and scaled limits. (English) Zbl 1056.15023 Nagoya Math. J. 174, 29-114 (2004). Reviewer: Martín Argerami (Regina) MSC: 15B52 60K35 33E17 34M55 34A05 15A18 82B43 PDFBibTeX XMLCite \textit{P. J. Forrester} and \textit{N. S. Witte}, Nagoya Math. J. 174, 29--114 (2004; Zbl 1056.15023) Full Text: DOI arXiv
Riaza, Ricardo A matrix pencil approach to the local stability analysis of nonlinear circuits. (English) Zbl 1037.94556 Int. J. Circuit Theory Appl. 32, No. 1, 23-46 (2004). MSC: 94C05 34M15 15A22 PDFBibTeX XMLCite \textit{R. Riaza}, Int. J. Circuit Theory Appl. 32, No. 1, 23--46 (2004; Zbl 1037.94556) Full Text: DOI
Crawley-Boevey, William On matrices in prescribed conjugacy classes with no common invariant subspace and sum zero. (English) Zbl 1046.15013 Duke Math. J. 118, No. 2, 339-352 (2003). Reviewer: Rodica Covaci (Cluj-Napoca) MSC: 15A24 16G20 34M50 15A18 PDFBibTeX XMLCite \textit{W. Crawley-Boevey}, Duke Math. J. 118, No. 2, 339--352 (2003; Zbl 1046.15013) Full Text: DOI arXiv
Forrester, P. J.; Witte, N. S. Discrete Painlevé equations and random matrix averages. (English) Zbl 1071.15026 Nonlinearity 16, No. 6, 1919-1944 (2003). MSC: 15B52 33E17 34M55 39A12 37F10 PDFBibTeX XMLCite \textit{P. J. Forrester} and \textit{N. S. Witte}, Nonlinearity 16, No. 6, 1919--1944 (2003; Zbl 1071.15026) Full Text: DOI arXiv
Bleher, Pavel; Eynard, Bertrand Double scaling limit in random matrix models and a nonlinear hierarchy of differential equations. (English) Zbl 1053.15017 J. Phys. A, Math. Gen. 36, No. 12, 3085-3105 (2003). Reviewer: Fabio L. Toninelli (Lyon) MSC: 15B52 82B44 82B41 34M30 37K10 PDFBibTeX XMLCite \textit{P. Bleher} and \textit{B. Eynard}, J. Phys. A, Math. Gen. 36, No. 12, 3085--3105 (2003; Zbl 1053.15017) Full Text: DOI arXiv
Forrester, P. J.; Frankel, N. E.; Garoni, T. M.; Witte, N. S. Painlevé transcendent evaluations of finite system density matrices for 1d impenetrable bosons. (English) Zbl 1041.82003 Commun. Math. Phys. 238, No. 1-2, 257-285 (2003). MSC: 82B10 34M55 15A15 82B23 82B44 PDFBibTeX XMLCite \textit{P. J. Forrester} et al., Commun. Math. Phys. 238, No. 1--2, 257--285 (2003; Zbl 1041.82003) Full Text: DOI arXiv
Forrester, P. J.; Witte, N. S. \(\tau\)-function evaluation of gap probabilities in orthogonal and symplectic matrix ensembles. (English) Zbl 1006.15028 Nonlinearity 15, No. 3, 937-954 (2002). Reviewer: Kim Hang Kim (Montgomery) MSC: 15B52 60K35 34M55 PDFBibTeX XMLCite \textit{P. J. Forrester} and \textit{N. S. Witte}, Nonlinearity 15, No. 3, 937--954 (2002; Zbl 1006.15028) Full Text: DOI arXiv
Baik, Jinho Painlevé expressions for LOE, LSE, and interpolating ensembles. (English) Zbl 1016.60018 Int. Math. Res. Not. 2002, No. 33, 1739-1789 (2002). MSC: 60E05 15B52 82B99 34M55 PDFBibTeX XMLCite \textit{J. Baik}, Int. Math. Res. Not. 2002, No. 33, 1739--1789 (2002; Zbl 1016.60018) Full Text: DOI arXiv
Tracy, Craig A.; Widom, Harold Airy kernel and Painlevé II. (English) Zbl 1174.82309 Harnad, John (ed.) et al., Isomonodromic deformations and applications in physics. CRM workshop, Montréal, Canada, May 1–6, 2000. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-2804-5/pbk). CRM Proc. Lect. Notes 31, 85-96 (2002). MSC: 82B41 15B52 33E17 34M55 60K35 PDFBibTeX XMLCite \textit{C. A. Tracy} and \textit{H. Widom}, CRM Proc. Lect. Notes 31, 85--96 (2002; Zbl 1174.82309) Full Text: arXiv
Forrester, P. J.; Witte, N. S. Application of the \(\tau\)-function theory of Painlevé equations to random matrices: PIV, PII and the GUE. (English) Zbl 1042.82019 Commun. Math. Phys. 219, No. 2, 357-398 (2001). MSC: 82B41 15B52 34M55 PDFBibTeX XMLCite \textit{P. J. Forrester} and \textit{N. S. Witte}, Commun. Math. Phys. 219, No. 2, 357--398 (2001; Zbl 1042.82019) Full Text: DOI arXiv
Ercolani, Nicholas M.; McLaughlin, Kenneth T.-R. Asymptotics and integrable structures for biorthogonal polynomials associated to a random two-matrix model. (English) Zbl 1038.82042 Physica D 152-153, 232-268 (2001). MSC: 82B44 42C05 15B52 33E99 34M50 37K10 PDFBibTeX XMLCite \textit{N. M. Ercolani} and \textit{K. T. R. McLaughlin}, Physica D 152--153, 232--268 (2001; Zbl 1038.82042) Full Text: DOI
Kostov, Vladimir Petrov Some examples of rigid representations. (English) Zbl 0974.15008 Serdica Math. J. 26, No. 3, 253-276 (2000). Reviewer: Vesselin Drensky (Sofia) MSC: 15A24 32S40 34M35 34M45 15A30 20G20 PDFBibTeX XMLCite \textit{V. P. Kostov}, Serdica Math. J. 26, No. 3, 253--276 (2000; Zbl 0974.15008) Full Text: arXiv EuDML
Forrester, P. J.; Witte, N. S. Exact Wigner surmise type evaluation of the spacing distribution in the bulk of the scaled random matrix ensembles. (English) Zbl 0978.15019 Lett. Math. Phys. 53, No. 3, 195-200 (2000). Reviewer: Michal Zajac (Bratislava) MSC: 15B52 82B41 81Q50 34M55 PDFBibTeX XMLCite \textit{P. J. Forrester} and \textit{N. S. Witte}, Lett. Math. Phys. 53, No. 3, 195--200 (2000; Zbl 0978.15019) Full Text: DOI arXiv
Witte, N. S.; Forrester, P. J. Gap probabilities in the finite and scaled Cauchy random matrix ensembles. (English) Zbl 0980.15018 Nonlinearity 13, No. 6, 1965-1986 (2000). Reviewer: Alexei Khorunzhy (Paris) MSC: 15B52 34A34 34M55 33C45 PDFBibTeX XMLCite \textit{N. S. Witte} and \textit{P. J. Forrester}, Nonlinearity 13, No. 6, 1965--1986 (2000; Zbl 0980.15018) Full Text: DOI arXiv
Witte, N. S.; Forrester, P. J.; Cosgrove, Christopher M. Gap probabilities for edge intervals in finite Gaussian and Jacobi unitary matrix ensembles. (English) Zbl 0970.15019 Nonlinearity 13, No. 5, 1439-1464 (2000). Reviewer: Alexei Khorunzhy (Paris) MSC: 15B52 15A18 34M55 PDFBibTeX XMLCite \textit{N. S. Witte} et al., Nonlinearity 13, No. 5, 1439--1464 (2000; Zbl 0970.15019) Full Text: DOI arXiv