Guera, Charlie Dworaczek; Memin, Ronan CLT for real \(\beta\)-ensembles at high temperature. (English) Zbl 07960005 Electron. J. Probab. 29, Paper No. 171, 45 p. (2024). MSC: 60B20 60F05 60K35 82B31 34K08 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Uwamariya, Denise; Yang, Xiangfeng On the ratio of extremal eigenvalues of \(\beta \)-Laguerre ensembles. (English) Zbl 07939843 Theory Probab. Math. Stat. 111, 167-179 (2024). MSC: 60B20 60F10 15A12 15A18 × Cite Format Result Cite Review PDF Full Text: DOI
Gorin, Vadim; Kleptsyn, Victor Universal objects of the infinite beta random matrix theory. (English) Zbl 1546.15025 J. Eur. Math. Soc. (JEMS) 26, No. 9, 3429-3496 (2024). MSC: 15B52 15A18 33C45 33C10 60B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Auer, Martin; Voit, Michael; Woerner, Jeannette H. C. Wigner- and marchenko-Pastur-type limit theorems for Jacobi processes. (English) Zbl 1541.60013 J. Theor. Probab. 37, No. 2, 1674-1709 (2024). MSC: 60F05 60F15 60J60 60K35 70F10 82C22 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Voit, Michael Freezing limits for Calogero-Moser-Sutherland particle models. (English) Zbl 1536.60073 Stud. Appl. Math. 151, No. 4, 1230-1281 (2023). MSC: 60J60 60B20 35R60 35K57 35Q70 82C22 60G15 33C10 33C52 33C47 × Cite Format Result Cite Review PDF Full Text: DOI
Gaudreau Lamarre, Pierre Yves; Ghosal, Promit; Li, Wenxuan; Liao, Yuchen Rigidity of the stochastic Airy operator. (English) Zbl 1537.60091 Int. Math. Res. Not. 2023, No. 24, 20701-20724 (2023). MSC: 60H25 47A10 47B80 60G55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Ruzza, Giulio Jacobi beta ensemble and \(b\)-Hurwitz numbers. (English) Zbl 1532.15030 SIGMA, Symmetry Integrability Geom. Methods Appl. 19, Paper 100, 18 p. (2023). Reviewer: Sho Matsumoto (Kagoshima) MSC: 15B52 60B20 05B20 05E05 05A15 05E16 33C80 60G55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ma, Yutao; Shen, Xinmei Approximation of beta-Jacobi ensembles by beta-Laguerre ensembles. (English) Zbl 1526.60008 Front. Math. (Beijing) 18, No. 1, 225-252 (2023). MSC: 60B20 60F99 62J10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dimitrov, Evgeni; Zhang, Hengzhi A global large deviation principle for discrete \(\beta \)-ensembles. (English) Zbl 1544.60032 Electron. J. Probab. 28, Paper No. 105, 28 p. (2023). Reviewer: Göran Högnäs (Åbo) MSC: 60F10 82B05 60B10 60B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Lambert, Gaultier; Paquette, Elliot Strong approximation of Gaussian \(\beta\) ensemble characteristic polynomials: the hyperbolic regime. (English) Zbl 1517.60013 Ann. Appl. Probab. 33, No. 1, 549-612 (2023). Reviewer: Guanggan Chen (Chengdu) MSC: 60B20 37H15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Min, Chao; Chen, Yang Global and local scaling limits for linear eigenvalue statistics of Jacobi \(\beta\)-ensembles. (English) Zbl 07827916 Basor, Estelle (ed.) et al., Toeplitz operators and random matrices. In memory of Harold Widom. Cham: Birkhäuser. Oper. Theory: Adv. Appl. 289, 531-559 (2022). MSC: 47B35 15B48 60B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Valkó, Benedek; Virág, Bálint The many faces of the stochastic zeta function. (English) Zbl 1509.11089 Geom. Funct. Anal. 32, No. 5, 1160-1231 (2022). Reviewer: Roma Kačinskaitė (Vilnius) MSC: 11M41 60B20 15B52 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Voit, Michael Freezing limits for beta-Cauchy ensembles. (English) Zbl 1498.60101 SIGMA, Symmetry Integrability Geom. Methods Appl. 18, Paper 069, 25 p. (2022). MSC: 60F05 60B20 70F10 82C22 33C45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Huang, Naqi; Ma, Yutao Limit theorems for \(\beta\)-Laguerre and \(\beta\)-Jacobi ensembles. (English) Zbl 1513.15059 Acta Math. Sci., Ser. B, Engl. Ed. 42, No. 5, 2025-2039 (2022). MSC: 15B52 60B20 60F10 × Cite Format Result Cite Review PDF Full Text: DOI Link
Gao, Fuqing; Mu, Jianyong Moderate deviations for linear eigenvalue statistics of \(\beta\)-ensembles. (English) Zbl 1490.60061 Random Matrices Theory Appl. 11, No. 2, Article ID 2250017, 29 p. (2022). Reviewer: Anatoliy Swishchuk (Calgary) MSC: 60F10 60K35 82B05 × Cite Format Result Cite Review PDF Full Text: DOI
Guionnet, Alice; Memin, Ronan Large deviations for Gibbs ensembles of the classical Toda chain. (English) Zbl 1487.60013 Electron. J. Probab. 27, Paper No. 46, 29 p. (2022). MSC: 60B20 60K35 60F10 × Cite Format Result Cite Review PDF Full Text: DOI
Das, Sayan; Dimitrov, Evgeni Large deviations for discrete \(\beta\)-ensembles. (English) Zbl 1501.60023 J. Funct. Anal. 283, No. 1, Article ID 109487, 108 p. (2022). Reviewer: Zakhar Kabluchko (Münster) MSC: 60F10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bourgade, Paul; Mody, Krishnan; Pain, Michel Optimal local law and central limit theorem for \(\beta\)-ensembles. (English) Zbl 1491.37051 Commun. Math. Phys. 390, No. 3, 1017-1079 (2022). Reviewer: Zakhar Kabluchko (Münster) MSC: 37H10 15B52 37A50 37A60 60B20 60F05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Voit, Michael; Woerner, Jeannette H. C. Limit theorems for Bessel and Dunkl processes of large dimensions and free convolutions. (English) Zbl 1479.60054 Stochastic Processes Appl. 143, 207-253 (2022). MSC: 60F05 60F15 60B20 60J60 60K35 70F10 82C22 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Charlier, Christophe; Claeys, Tom Global rigidity and exponential moments for soft and hard edge point processes. (English) Zbl 1512.60030 Probab. Math. Phys. 2, No. 2, 143-197 (2021). MSC: 60G55 33B15 33C10 35Q15 60B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Lupu, Titus Isomorphisms of \(\beta\)-Dyson’s Brownian motion with Brownian local time. (English) Zbl 1484.60084 Electron. J. Probab. 26, Paper No. 126, 31 p. (2021). MSC: 60J55 60J65 60G15 60B20 81T18 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hermann, Kilian; Voit, Michael Limit theorems for Jacobi ensembles with large parameters. (English) Zbl 1496.33010 Tunis. J. Math. 3, No. 4, 843-860 (2021). MSC: 33C45 33C67 60B20 60F05 70F10 82C22 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Trinh, Hoang Dung; Trinh, Khanh Duy Beta Jacobi ensembles and associated Jacobi polynomials. (English) Zbl 1477.60021 J. Stat. Phys. 185, No. 1, Paper No. 4, 15 p. (2021). Reviewer: Olivier Marchal (Saint-Etienne) MSC: 60B20 15A18 15B52 60K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Assiotis, Theodoros; Najnudel, Joseph The boundary of the orbital beta process. (English) Zbl 1473.60113 Mosc. Math. J. 21, No. 4, 659-694 (2021). MSC: 60J50 60B20 60F15 60J05 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Lambert, Gaultier Poisson statistics for Gibbs measures at high temperature. (English. French summary) Zbl 1473.60019 Ann. Inst. Henri Poincaré, Probab. Stat. 57, No. 1, 326-350 (2021). Reviewer: Julien Poisat (Paris) MSC: 60B20 60G55 82B31 60G70 60F10 82D05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Lambert, Gaultier Mesoscopic central limit theorem for the circular \(\beta\)-ensembles and applications. (English) Zbl 1468.60033 Electron. J. Probab. 26, Paper No. 7, 33 p. (2021). MSC: 60F05 60G20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Basu, Riddhipratim; Ganguly, Shirshendu; Hegde, Milind; Krishnapur, Manjunath Lower deviations in \(\beta \)-ensembles and law of iterated logarithm in last passage percolation. (English) Zbl 1489.60152 Isr. J. Math. 242, No. 1, 291-324 (2021). MSC: 60K35 60B20 60F15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Backlinks: MO
Olshanski, Grigori Macdonald-level extension of beta ensembles and large-\(N\) limit transition. (English) Zbl 1469.82023 Commun. Math. Phys. 385, No. 1, 595-631 (2021). MSC: 82C22 15B52 33C47 60B20 60G55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Trinh, Hoang Dung; Trinh, Khanh Duy Beta Laguerre processes in a high temperature regime. (English) Zbl 1469.60349 Stochastic Processes Appl. 136, 192-205 (2021). MSC: 60K35 60F05 60H05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gautier, Guillaume; Bardenet, Rémi; Valko, Michal Fast sampling from \(\beta \)-ensembles. (English) Zbl 1462.62025 Stat. Comput. 31, No. 1, Paper No. 7, 20 p. (2021). MSC: 62-08 60K35 65C40 60B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Forrester, Peter J.; Liu, Dang-Zheng Phase transitions for products of characteristic polynomials under Dyson Brownian motion. (English) Zbl 1480.60246 Acta Math. Sin., Engl. Ser. 37, No. 3, 509-524 (2021). MSC: 60J65 15B52 37H10 11M26 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hardy, Adrien; Lambert, Gaultier CLT for circular beta-ensembles at high temperature. (English) Zbl 1469.60032 J. Funct. Anal. 280, No. 7, Article ID 108869, 41 p. (2021). MSC: 60B20 60F05 15B52 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Voit, Michael Some martingales associated with multivariate Jacobi processes and Aomoto’s Selberg integral. (English) Zbl 1445.60056 Indag. Math., New Ser. 31, No. 3, 398-410 (2020). MSC: 60J60 33B15 33C45 05A15 82B41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Nakano, Fumihiko; Trinh, Khanh Duy Poisson statistics for beta ensembles on the real line at high temperature. (English) Zbl 1437.60014 J. Stat. Phys. 179, No. 2, 632-649 (2020). MSC: 60F05 60B20 60G55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chen, Lei; Wang, Shaochen Moderate deviations for extreme eigenvalues of beta-Laguerre ensembles. (English) Zbl 1434.60021 Random Matrices Theory Appl. 9, No. 2, Article ID 2050003, 20 p. (2020). MSC: 60B20 65F15 × Cite Format Result Cite Review PDF Full Text: DOI
Pakzad, Cambyse Large deviations principle for the largest eigenvalue of the Gaussian \(\beta \)-ensemble at high temperature. (English) Zbl 1431.60008 J. Theor. Probab. 33, No. 1, 428-443 (2020). MSC: 60B20 60F10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Holcomb, Diane; Virág, Bálint A short introduction to operator limits of random matrices. (English) Zbl 1494.60010 Borodin, Alexei (ed.) et al., Random matrices. Providence, RI: American Mathematical Society (AMS); Princeton, NJ: Institute for Advanced Study (IAS). IAS/Park City Math. Ser. 26, 213-250 (2019). MSC: 60B20 15B52 60-01 × Cite Format Result Cite Review PDF
Lambert, Gaultier; Ledoux, Michel; Webb, Christian Quantitative normal approximation of linear statistics of \(\beta \)-ensembles. (English) Zbl 1448.60058 Ann. Probab. 47, No. 5, 2619-2685 (2019). MSC: 60F05 60B20 60K35 15B52 82B05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Lamarre, Pierre Yves Gaudreau; Shkolnikov, Mykhaylo Edge of spiked beta ensembles, stochastic Airy semigroups and reflected Brownian motions. (English. French summary) Zbl 1447.60024 Ann. Inst. Henri Poincaré, Probab. Stat. 55, No. 3, 1402-1438 (2019). MSC: 60B20 60H25 47D08 60J55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Guionnet, Alice; Huang, Jiaoyang Rigidity and edge universality of discrete \(\beta\)-ensembles. (English) Zbl 1455.60014 Commun. Pure Appl. Math. 72, No. 9, 1875-1982 (2019). MSC: 60B20 60E05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Rider, Brian; Waters, Patrick Universality of the stochastic Bessel operator. (English) Zbl 1422.60037 Probab. Theory Relat. Fields 175, No. 1-2, 97-140 (2019). MSC: 60F05 60H25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Pakzad, Cambyse Poisson statistics at the edge of Gaussian \(\beta\)-ensemble at high temperature. (English) Zbl 1422.60018 ALEA, Lat. Am. J. Probab. Math. Stat. 16, No. 1, 871-897 (2019). MSC: 60B20 15B52 60F05 60G70 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Trinh, Khanh Duy Global spectrum fluctuations for Gaussian beta ensembles: a martingale approach. (English) Zbl 1447.60030 J. Theor. Probab. 32, No. 3, 1420-1437 (2019). MSC: 60B20 60F05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Guionnet, Alice Asymptotics of random matrices and related models. The uses of Dyson-Schwinger equations. (English) Zbl 1464.60004 CBMS Regional Conference Series in Mathematics 130. Providence, RI: American Mathematical Society (AMS), published for the Conference Board of the Mathematical Sciences (CBMS) (ISBN 978-1-4704-5027-4/pbk; 978-1-4704-5194-3/ebook). vii, 143 p. (2019). Reviewer: Michael Voit (Dortmund) MSC: 60-02 60B20 60F05 60F10 46L54 × Cite Format Result Cite Review PDF Full Text: DOI
Unterberger, Jeremie Global fluctuations for 1D log-gas dynamics. Covariance kernel and support. (English) Zbl 1412.60017 Electron. J. Probab. 24, Paper No. 21, 28 p. (2019). MSC: 60B20 15B52 60F05 60G20 60J60 60J75 60K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Bekerman, Florent; Leblé, Thomas; Serfaty, Sylvia CLT for fluctuations of \(\beta \)-ensembles with general potential. (English) Zbl 1406.60036 Electron. J. Probab. 23, Paper No. 115, 31 p. (2018). MSC: 60F05 60K35 60B10 60B20 15B52 82B05 60G15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Augeri, Fanny On the large deviations of traces of random matrices. (English. French summary) Zbl 1417.60005 Ann. Inst. Henri Poincaré, Probab. Stat. 54, No. 4, 2239-2285 (2018). MSC: 60B20 60F10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Unterberger, Jérémie Global fluctuations for 1D log-gas dynamics. (English) Zbl 1417.60009 Stochastic Processes Appl. 128, No. 12, 4104-4153 (2018). MSC: 60B20 60F05 60J60 60J75 60K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Nakano, Fumihiko; Trinh, Khanh Duy Gaussian beta ensembles at high temperature: eigenvalue fluctuations and bulk statistics. (English) Zbl 1403.60013 J. Stat. Phys. 173, No. 2, 295-321 (2018). MSC: 60B20 82B44 60F05 60G55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dubach, Guillaume Powers of Ginibre eigenvalues. (English) Zbl 1402.60008 Electron. J. Probab. 23, Paper No. 111, 31 p. (2018). MSC: 60B20 15B52 15A18 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Chhaibi, Reda; Madaule, Thomas; Najnudel, Joseph On the maximum of the C\(\beta\)E field. (English) Zbl 1457.60008 Duke Math. J. 167, No. 12, 2243-2345 (2018). Reviewer: Vakhtang V. Kvaratskhelia (Tbilisi) MSC: 60B20 60G70 15B52 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Carroll, Tom; Marzo, Jordi; Massaneda, Xavier; Ortega-Cerdà, Joaquim Equidistribution and \(\beta\)-ensembles. (English. French summary) Zbl 1410.60010 Ann. Fac. Sci. Toulouse, Math. (6) 27, No. 2, 377-387 (2018). MSC: 60B20 15B52 × Cite Format Result Cite Review PDF Full Text: arXiv
Adhikari, Kartick Hole probabilities for \(\beta\)-ensembles and determinantal point processes in the complex plane. (English) Zbl 1410.60048 Electron. J. Probab. 23, Paper No. 48, 21 p. (2018). MSC: 60G55 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Leblé, Thomas; Serfaty, Sylvia Fluctuations of two dimensional Coulomb gases. (English) Zbl 1423.60045 Geom. Funct. Anal. 28, No. 2, 443-508 (2018). Reviewer: Fraser Daly (Edinburgh) MSC: 60F05 60K35 82B05 60G15 62E20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bekerman, Florent Transport maps for \(\beta\)-matrix models in the multi-cut regime. (English) Zbl 1390.60028 Random Matrices Theory Appl. 7, No. 1, Article ID 1750013, 36 p. (2018). MSC: 60B20 60F05 60K35 60B10 82B05 60G15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Forrester, Peter J.; Rahman, Anas A.; Witte, Nicholas S. Large \(N\) expansions for the Laguerre and Jacobi \(\beta\)-ensembles from the loop equations. (English) Zbl 1384.82012 J. Math. Phys. 58, No. 11, 113303, 25 p. (2017). Reviewer: Guy Jumarie (Montréal) MSC: 82C70 15B52 47A10 11M36 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kozhan, Rostyslav Rank one non-Hermitian perturbations of Hermitian \(\beta \)-ensembles of random matrices. (English) Zbl 1372.15030 J. Stat. Phys. 168, No. 1, 92-108 (2017). MSC: 15B52 15A18 15A03 60B20 × Cite Format Result Cite Review PDF Full Text: DOI
Valkó, Benedek; Virág, Bálint The \(\mathrm{Sine}_{\beta}\) operator. (English) Zbl 1443.60008 Invent. Math. 209, No. 1, 275-327 (2017). MSC: 60B20 60H25 60G55 60J65 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Holcomb, Diane; Valkó, Benedek Overcrowding asymptotics for the \(\mathrm{Sine}_\beta\) process. (English. French summary) Zbl 1381.60021 Ann. Inst. Henri Poincaré, Probab. Stat. 53, No. 3, 1181-1195 (2017). MSC: 60B20 60F10 15B52 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Borodin, Alexei; Gorin, Vadim; Guionnet, Alice Gaussian asymptotics of discrete \(\beta \)-ensembles. (English) Zbl 1406.60008 Publ. Math., Inst. Hautes Étud. Sci. 125, 1-78 (2017). MSC: 60B10 60B20 81R12 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mezzadri, Francesco; Reynolds, Alexi K.; Winn, Brian Moments of the eigenvalue densities and of the secular coefficients of \(\beta\)-ensembles. (English) Zbl 1362.15027 Nonlinearity 30, No. 3, 1034-1057 (2017). MSC: 15B52 05E05 33C45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Domínguez-Molina, J. Armando The Tracy-Widom distribution is not infinitely divisible. (English) Zbl 1416.60016 Stat. Probab. Lett. 123, 56-60 (2017). MSC: 60B20 60E07 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Liu, Dang-Zheng Limits for circular Jacobi beta-ensembles. (English) Zbl 1364.60016 J. Approx. Theory 215, 40-67 (2017). Reviewer: Olivier Marchal (Saint-Etienne) MSC: 60B20 33C75 41A60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Marinello, G.; Pato, M. P. A pseudo-Hermitian \(\beta\)-Hermite family of matrices. (English) Zbl 1400.15037 Physica A 444, 1049-1061 (2016). MSC: 15B52 60B20 81R12 × Cite Format Result Cite Review PDF Full Text: DOI
Donati-Martin, Catherine; Rouault, Alain Near-extreme eigenvalues in the beta-ensembles. (English) Zbl 1346.15034 Electron. J. Probab. 21, Paper No. 52, 17 p. (2016). MSC: 15B52 60G57 60F10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Jiang, Hui; Wang, Shaochen Moderate deviation principles for eigenvalues of \(\beta\)-Hermite and \(\beta\)-Laguerre ensembles with \(\beta \to \infty\). (English) Zbl 1375.60069 Stat. Probab. Lett. 118, 50-59 (2016). MSC: 60F10 60B20 15B52 × Cite Format Result Cite Review PDF Full Text: DOI
Shcherbina, M. Fluctuations of the eigenvalue number in the fixed interval for \(\beta\)-models with \(\beta = 1, 2, 4\). (English) Zbl 1369.15023 Agliari, Elena (ed.) et al., Theory and applications in mathematical physics. Conference in honor of B. Tirozzi’s 70th birthday. Hackensack, NJ: World Scientific (ISBN 978-981-4713-27-6/hbk; 978-981-4713-29-0/ebook). 131-146 (2016). MSC: 15B52 15A18 60B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Han, Dong; Zhang, Deng Limiting spectral distribution of random birth-death \(Q\) matrices. (Chinese. English summary) Zbl 1488.60007 Sci. Sin., Math. 45, No. 5, 539-558 (2015). MSC: 60B20 60F05 62M15 × Cite Format Result Cite Review PDF Full Text: DOI
Benaych-Georges, Florent; Péché, Sandrine Poisson statistics for matrix ensembles at large temperature. (English) Zbl 1329.82055 J. Stat. Phys. 161, No. 3, 633-656 (2015). MSC: 82B41 15B52 60F05 60G55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fan, C.; Guionnet, A.; Song, Y.; Wang, A. Convergence of eigenvalues to the support of the limiting measure in critical \(\beta\) matrix models. (English) Zbl 1331.60018 Random Matrices Theory Appl. 4, No. 3, Article ID 1550013, 22 p. (2015). MSC: 60B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Desrosiers, Patrick; Liu, Dang-Zheng Selberg integrals, super-hypergeometric functions and applications to \(\beta\)-ensembles of random matrices. (English) Zbl 1328.15049 Random Matrices Theory Appl. 4, No. 2, Article ID 1550007, 59 p. (2015). Reviewer: Andreas Arvanitoyeorgos (Patras) MSC: 15B52 05E05 33C70 60B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Borodin, Alexei; Gorin, Vadim General \(\beta\)-Jacobi corners process and the Gaussian free field. (English) Zbl 1325.60076 Commun. Pure Appl. Math. 68, No. 10, 1774-1844 (2015). MSC: 60G60 60B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Erdős, László; Yau, Horng-Tzer Gap universality of generalized Wigner and \(\beta\)-ensembles. (English) Zbl 1333.15031 J. Eur. Math. Soc. (JEMS) 17, No. 8, 1927-2036 (2015). Reviewer: Anouar Ben Mabrouk (Sousse) MSC: 15B52 81S30 82B44 60B20 60J65 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Rumanov, Igor Classical integrability for beta-ensembles and general Fokker-Planck equations. (English) Zbl 1309.82026 J. Math. Phys. 56, No. 1, 013508, 16 p. (2015). MSC: 82C31 35Q84 81T40 15B52 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Xie, Junshan; Zhao, Jing A result on precise asymptotics for largest eigenvalues of \(\beta\) ensembles. (English) Zbl 1333.60059 J. Inequal. Appl. 2014, Paper No. 408, 10 p. (2014). MSC: 60F15 60G50 60G70 × Cite Format Result Cite Review PDF Full Text: DOI
Forrester, Peter J. Asymptotics of spacing distributions 50 years later. (English) Zbl 1360.60017 Deift, Percy (ed.) et al., Random matrix theory, interacting particle systems and integrable systems. New York, NY: Cambridge University Press (ISBN 978-1-107-07992-2/hbk). Mathematical Sciences Research Institute Publications 65, 199-222 (2014). MSC: 60B20 15B52 60-03 × Cite Format Result Cite Review PDF Full Text: arXiv
Desrosiers, Patrick; Liu, Dang-Zheng Asymptotics for products of characteristic polynomials in classical \(\beta\)-ensembles. (English) Zbl 1311.15033 Constr. Approx. 39, No. 2, 273-322 (2014). Reviewer: Francisco Marcellán (Leganes) MSC: 15B52 05E05 33C70 60B20 15A18 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Allez, Romain; Dumaz, Laure Tracy-Widom at high temperature. (English) Zbl 1309.82019 J. Stat. Phys. 156, No. 6, 1146-1183 (2014). Reviewer: Utkir A. Rozikov (Tashkent) MSC: 82B44 15B52 60G70 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bourgade, P. Bulk universality for one-dimensional log-gases. (English) Zbl 1304.82018 Jensen, Arne (ed.), XVIIth international congress on mathematical physics, Aalborg, Denmark, August 6–11, 2012. Hackensack, NJ: World Scientific (ISBN 978-981-4449-23-6/hbk; 978-981-4449-25-0/ebook). 404-416 (2014). MSC: 82B21 82B31 15B52 × Cite Format Result Cite Review PDF Full Text: DOI Link
Gelbaum, Zachary On the largest eigenvalue of products from the \(\beta\)-Laguerre ensemble. (English) Zbl 1315.60006 Random Matrices Theory Appl. 3, No. 2, Article ID 1450008, 14 p. (2014). MSC: 60B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Andraus, Sergio; Katori, Makoto; Miyashita, Seiji Two limiting regimes of interacting Bessel processes. (English) Zbl 1296.15018 J. Phys. A, Math. Theor. 47, No. 23, Article ID 235201, 30 p. (2014). Reviewer: A. Arvanitoyeorgos (Patras) MSC: 15B52 33C10 33C45 42C05 60B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dubbs, Alexander; Edelman, Alan The beta-MANOVA ensemble with general covariance. (English) Zbl 1291.62114 Random Matrices Theory Appl. 3, No. 1, Article ID 1450002, 16 p. (2014). MSC: 62H12 15B52 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sosoe, Philippe; Wong, Percy Convergence of the eigenvalue density for Laguerre beta ensembles on short scales. (English) Zbl 1310.60004 Electron. J. Probab. 19, Paper No. 34, 18 p. (2014). MSC: 60B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Venker, Martin Particle systems with repulsion exponent \(\beta\) and random matrices. (English) Zbl 1297.15040 Electron. Commun. Probab. 18, Paper No. 83, 12 p. (2013). MSC: 15B52 60B20 82C22 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Forrester, Peter J. Probability densities and distributions for spiked and general variance Wishart \(\beta\)-ensembles. (English) Zbl 1281.15042 Random Matrices Theory Appl. 2, No. 4, Article ID 1350011, 19 p. (2013). MSC: 15B52 15A18 60B20 33E17 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bufetov, Alexander; Mkrtchyan, Sevak; Shcherbina, Maria; Soshnikov, Alexander Entropy and the Shannon-McMillan-Breiman theorem for beta random matrix ensembles. (English) Zbl 1283.60012 J. Stat. Phys. 152, No. 1, 1-14 (2013). MSC: 60B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Dumaz, Laure; Virág, Bálint The right tail exponent of the Tracy-Widom \(\beta\) distribution. (English. French summary) Zbl 1278.60012 Ann. Inst. Henri Poincaré, Probab. Stat. 49, No. 4, 915-933 (2013). MSC: 60B20 60F10 60H25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Zeng, Xingyuan; Hou, Zhenting Precise asymptotics for beta ensembles. (English) Zbl 1276.15020 Indian J. Pure Appl. Math. 44, No. 3, 383-404 (2013). Reviewer: Václav Burjan (Praha) MSC: 15B52 60B20 15A42 × Cite Format Result Cite Review PDF Full Text: DOI
Holcomb, Diane; Moreno Flores, Gregorio R. Edge scaling of the \(\beta\)-Jacobi ensemble. (English) Zbl 1257.82006 J. Stat. Phys. 149, No. 6, 1136-1160 (2012). MSC: 82B05 15B52 60B20 60F05 60H25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wong, Percy Local semicircle law at the spectral edge for Gaussian \(\beta \)-ensembles. (English) Zbl 1251.82031 Commun. Math. Phys. 312, No. 1, 251-263 (2012). MSC: 82B44 15B52 60B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Forrester, Peter J. Large deviation eigenvalue density for the soft edge Laguerre and Jacobi \(\beta \)-ensembles. (English) Zbl 1241.82007 J. Phys. A, Math. Theor. 45, No. 14, Article ID 145201, 15 p. (2012). MSC: 82B05 15B52 15A18 60F10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Forrester, Peter J. Spectral density asymptotics for Gaussian and Laguerre \(\beta \)-ensembles in the exponentially small region. (English) Zbl 1237.15032 J. Phys. A, Math. Theor. 45, No. 7, Article ID 075206, 17 p. (2012). MSC: 15B52 15A18 60B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gamboa, Fabrice; Rouault, Alain Large deviations for random spectral measures and sum rules. (English) Zbl 1261.60008 AMRX, Appl. Math. Res. Express 2011, 281-307 (2011). Reviewer: Michael Stolz (Bochum) MSC: 60B20 60F10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Su, Zhonggen On the second-order correlation of characteristic polynomials of Hermite \(\beta \) ensembles. (English) Zbl 1204.15046 Stat. Probab. Lett. 80, No. 19-20, 1500-1507 (2010). Reviewer: Václav Burjan (Praha) MSC: 15B52 60B20 × Cite Format Result Cite Review PDF Full Text: DOI
Valkó, Benedek; Virág, Bálint Large gaps between random eigenvalues. (English) Zbl 1223.60009 Ann. Probab. 38, No. 3, 1263-1279 (2010). Reviewer: Michael Stolz (Bochum) MSC: 60B20 60F10 60H30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Su, ZhongGen Circular \(\beta \) ensembles, CMV representation, characteristic polynomials. (English) Zbl 1179.15038 Sci. China, Ser. A 52, No. 7, 1467-1477 (2009). Reviewer: Václav Burjan (Praha) MSC: 15B52 × Cite Format Result Cite Review PDF Full Text: DOI
Sinclair, Christopher D. Correlation functions for \(\beta =1\) ensembles of matrices of odd size. (English) Zbl 1220.82066 J. Stat. Phys. 136, No. 1, 17-33 (2009). MSC: 82B44 15B52 60B20 60K40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Albrecht, James T.; Chan, Cy P.; Edelman, Alan Sturm sequences and random eigenvalue distributions. (English) Zbl 1173.65027 Found. Comput. Math. 9, No. 4, 461-483 (2009). Reviewer: Václav Burjan (Praha) MSC: 65F15 15B52 15A18 × Cite Format Result Cite Review PDF Full Text: DOI Link
Valkó, Benedek; Virág, Bálint Continuum limits of random matrices and the Brownian carousel. (English) Zbl 1204.60012 Invent. Math. 177, No. 3, 463-508 (2009). Reviewer: Vakhtang V. Kvaratskhelia (Tbilisi) MSC: 60B20 60F10 15B52 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dumitriu, Ioana; Koev, Plamen Distributions of the extreme eigenvalues of beta-Jacobi random matrices. (English) Zbl 1158.15304 SIAM J. Matrix Anal. Appl. 30, No. 1, 1-6 (2008). MSC: 15B52 60E05 62H10 65F15 × Cite Format Result Cite Review PDF Full Text: DOI