Oussi, Lahcen Distribution for non symmetric position operators on the free toy Fock space and its approximation on the full Fock space. (English) Zbl 07757931 Complex Anal. Oper. Theory 17, No. 7, Paper No. 117, 20 p. (2023). Reviewer: Alexander Belton (Plymouth) MSC: 46L53 46L54 60F05 05A17 PDFBibTeX XMLCite \textit{L. Oussi}, Complex Anal. Oper. Theory 17, No. 7, Paper No. 117, 20 p. (2023; Zbl 07757931) Full Text: DOI OA License
Hasebe, Takahiro; Lehner, Franz Cumulants, spreadability and the Campbell-Baker-Hausdorff series. (English) Zbl 07753232 Doc. Math. 28, No. 3, 515-601 (2023). MSC: 46L53 60C05 17B01 05A18 PDFBibTeX XMLCite \textit{T. Hasebe} and \textit{F. Lehner}, Doc. Math. 28, No. 3, 515--601 (2023; Zbl 07753232) Full Text: DOI arXiv
Defant, Colin Fertilitopes. (English) Zbl 1523.52018 Discrete Comput. Geom. 70, No. 3, 713-752 (2023). MSC: 52B12 52B40 05A05 05A19 46L53 PDFBibTeX XMLCite \textit{C. Defant}, Discrete Comput. Geom. 70, No. 3, 713--752 (2023; Zbl 1523.52018) Full Text: DOI arXiv OA License
Bożejko, Marek; Ejsmont, Wiktor The double Fock space of type B. (English) Zbl 07711520 SIGMA, Symmetry Integrability Geom. Methods Appl. 19, Paper 040, 22 p. (2023). MSC: 46L53 46L54 20F55 81S25 05A15 43A35 PDFBibTeX XMLCite \textit{M. Bożejko} and \textit{W. Ejsmont}, SIGMA, Symmetry Integrability Geom. Methods Appl. 19, Paper 040, 22 p. (2023; Zbl 07711520) Full Text: DOI arXiv
Celestino, Adrian; Ebrahimi-Fard, Kurusch Conditionally monotone cumulants via shuffle algebra. arXiv:2312.04614 Preprint, arXiv:2312.04614 [math.OA] (2023). MSC: 05E99 16T30 17A30 46L53 BibTeX Cite \textit{A. Celestino} and \textit{K. Ebrahimi-Fard}, ``Conditionally monotone cumulants via shuffle algebra'', Preprint, arXiv:2312.04614 [math.OA] (2023) Full Text: arXiv OA License
Celestino, Adrian; Vargas, Yannic Schröder trees, antipode formulas and non-commutative probability. arXiv:2311.07824 Preprint, arXiv:2311.07824 [math.CO] (2023). MSC: 05E99 16T05 16T30 17A30 46L53 BibTeX Cite \textit{A. Celestino} and \textit{Y. Vargas}, ``Schr\"oder trees, antipode formulas and non-commutative probability'', Preprint, arXiv:2311.07824 [math.CO] (2023) Full Text: arXiv OA License
Adhikari, Arka; Dembo, Amir Spectral measure for uniform \(d\)-regular digraphs. arXiv:2310.14132 Preprint, arXiv:2310.14132 [math.PR] (2023). MSC: 46L53 60B10 60B20 05C50 05C20 BibTeX Cite \textit{A. Adhikari} and \textit{A. Dembo}, ``Spectral measure for uniform $d$-regular digraphs'', Preprint, arXiv:2310.14132 [math.PR] (2023) Full Text: arXiv OA License
Griseta, Maria Elena On non-commutative spreadability. arXiv:2310.04449 Preprint, arXiv:2310.04449 [math.OA] (2023). MSC: 60G09 05A99 16S35 46L53 46L55 46L30 BibTeX Cite \textit{M. E. Griseta}, ``On non-commutative spreadability'', Preprint, arXiv:2310.04449 [math.OA] (2023) Full Text: arXiv OA License
Krishnan, Arundhathi A central limit theorem in the framework of the Thompson group \(F\). arXiv:2309.05626 Preprint, arXiv:2309.05626 [math.OA] (2023). MSC: 46L53 60F05 05E16 20M05 68Q42 68R15 BibTeX Cite \textit{A. Krishnan}, ``A central limit theorem in the framework of the Thompson group $F$'', Preprint, arXiv:2309.05626 [math.OA] (2023) Full Text: arXiv OA License
Lenczewski, Romuald Decomposition of free cumulants. arXiv:2307.02281 Preprint, arXiv:2307.02281 [math.OA] (2023). MSC: 46L53 46L54 05A18 BibTeX Cite \textit{R. Lenczewski}, ``Decomposition of free cumulants'', Preprint, arXiv:2307.02281 [math.OA] (2023) Full Text: arXiv OA License
Gerhold, Malte; Varšo, Philipp Towards a classification of multi-faced independences: a combinatorial approach. arXiv:2301.01816 Preprint, arXiv:2301.01816 [math.FA] (2023). MSC: 46L53 05A18 60A05 18M05 46L54 BibTeX Cite \textit{M. Gerhold} and \textit{P. Varšo}, ``Towards a classification of multi-faced independences: a combinatorial approach'', Preprint, arXiv:2301.01816 [math.FA] (2023) Full Text: arXiv OA License
Arizmendi, Octavio; Celestino, Adrian Monotone cumulant-moment formula and Schröder trees. (English) Zbl 1516.16026 SIGMA, Symmetry Integrability Geom. Methods Appl. 18, Paper 073, 22 p. (2022). Reviewer: Loïc Foissy (Calais) MSC: 16T05 05C05 17A30 46L53 PDFBibTeX XMLCite \textit{O. Arizmendi} and \textit{A. Celestino}, SIGMA, Symmetry Integrability Geom. Methods Appl. 18, Paper 073, 22 p. (2022; Zbl 1516.16026) Full Text: DOI arXiv
Campbell, Jacob; Köstler, Claus; Nica, Alexandru A central limit theorem for star-generators of \(S_\infty\), which relates to traceless CCR-GUE matrices. (English) Zbl 1507.46042 Int. J. Math. 33, No. 9, Article ID 2250065, 46 p. (2022). Reviewer: Adam Skalski (Warszawa) MSC: 46L53 05A18 20C32 PDFBibTeX XMLCite \textit{J. Campbell} et al., Int. J. Math. 33, No. 9, Article ID 2250065, 46 p. (2022; Zbl 1507.46042) Full Text: DOI arXiv
Gilliers, Nicolas A shuffle algebra point of view on operator-valued probability theory. (English) Zbl 1502.18040 Adv. Math. 408, Part B, Article ID 108614, 44 p. (2022). Reviewer: Loïc Foissy (Calais) MSC: 18M50 46L53 46L54 17A30 18M60 05A17 16T30 PDFBibTeX XMLCite \textit{N. Gilliers}, Adv. Math. 408, Part B, Article ID 108614, 44 p. (2022; Zbl 1502.18040) Full Text: DOI arXiv
Oussi, Lahcen; Wysoczański, Janusz Analogues of Poisson type limit theorems in discrete bm-Fock spaces. arXiv:2210.12559 Preprint, arXiv:2210.12559 [math.CO] (2022). MSC: 46L53 05A18 30H20 60F05 BibTeX Cite \textit{L. Oussi} and \textit{J. Wysoczański}, ``Analogues of Poisson type limit theorems in discrete bm-Fock spaces'', Preprint, arXiv:2210.12559 [math.CO] (2022) Full Text: DOI arXiv OA License
Koohestani, Masoumeh; Obata, Nobuaki; Tanaka, Hajime Scaling limits for the Gibbs states on distance-regular graphs with classical parameters. (English) Zbl 1492.46057 SIGMA, Symmetry Integrability Geom. Methods Appl. 17, Paper 104, 22 p. (2021). Reviewer: Alexander Belton (Plymouth) MSC: 46L53 60F05 05E30 PDFBibTeX XMLCite \textit{M. Koohestani} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 17, Paper 104, 22 p. (2021; Zbl 1492.46057) Full Text: DOI arXiv
Cho, Ilwoo; Jorgensen, Palle E. T. The semicircular law of free probability as noncommutative multivariable operator theory. (English) Zbl 1490.46064 Adv. Oper. Theory 6, No. 4, Paper No. 69, 40 p. (2021). MSC: 46L53 47A13 05C62 17A50 18B40 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. E. T. Jorgensen}, Adv. Oper. Theory 6, No. 4, Paper No. 69, 40 p. (2021; Zbl 1490.46064) Full Text: DOI
Crismale, Vitonofrio; Griseta, Maria Elena; Wysoczański, Janusz Distributions for nonsymmetric monotone and weakly monotone position operators. (English) Zbl 1481.46069 Complex Anal. Oper. Theory 15, No. 6, Paper No. 101, 26 p. (2021). Reviewer: Adam Skalski (Warszawa) MSC: 46L53 60B99 05A18 PDFBibTeX XMLCite \textit{V. Crismale} et al., Complex Anal. Oper. Theory 15, No. 6, Paper No. 101, 26 p. (2021; Zbl 1481.46069) Full Text: DOI arXiv
Davis, Ethan; Jekel, David; Wang, Zhichao Tree convolution for probability distributions with unbounded support. (English) Zbl 1481.46070 ALEA, Lat. Am. J. Probab. Math. Stat. 18, No. 2, 1585-1623 (2021). MSC: 46L53 46L54 05C76 60F05 60E07 PDFBibTeX XMLCite \textit{E. Davis} et al., ALEA, Lat. Am. J. Probab. Math. Stat. 18, No. 2, 1585--1623 (2021; Zbl 1481.46070) Full Text: arXiv Link
Blitvić, Natasha; Steingrímsson, Einar Permutations, moments, measures. (English) Zbl 1469.05002 Trans. Am. Math. Soc. 374, No. 8, 5473-5508 (2021). MSC: 05A05 05A19 05A18 33C45 46L53 PDFBibTeX XMLCite \textit{N. Blitvić} and \textit{E. Steingrímsson}, Trans. Am. Math. Soc. 374, No. 8, 5473--5508 (2021; Zbl 1469.05002) Full Text: DOI arXiv Link
Saigo, Hayato Category Algebras and States on Categories. arXiv:2105.13642 Preprint, arXiv:2105.13642 [math.CT] (2021). MSC: 46L53 20L99 18E99 05A40 05A99 15A99 16D20 BibTeX Cite \textit{H. Saigo}, ``Category Algebras and States on Categories'', Preprint, arXiv:2105.13642 [math.CT] (2021) Full Text: arXiv OA License
Jekel, David; Liu, Weihua An operad of non-commutative independences defined by trees. (English) Zbl 1472.46068 Diss. Math. 553, 1-100 (2020). MSC: 46L53 46L54 05C76 60E07 PDFBibTeX XMLCite \textit{D. Jekel} and \textit{W. Liu}, Diss. Math. 553, 1--100 (2020; Zbl 1472.46068) Full Text: DOI arXiv
Dacko, Adrian \(V\)-monotone independence. (English) Zbl 1457.46066 Colloq. Math. 162, No. 1, 77-107 (2020). Reviewer: Alexander Belton (Lancaster) MSC: 46L53 05A18 PDFBibTeX XMLCite \textit{A. Dacko}, Colloq. Math. 162, No. 1, 77--107 (2020; Zbl 1457.46066) Full Text: DOI arXiv
Morales, John Vincent S.; Obata, Nobuaki; Tanaka, Hajime Asymptotic joint spectra of Cartesian powers of strongly regular graphs and bivariate Charlier-Hermite polynomials. (English) Zbl 1457.46067 Colloq. Math. 162, No. 1, 1-22 (2020). Reviewer: Adam Skalski (Warszawa) MSC: 46L53 05E30 33C45 60F05 PDFBibTeX XMLCite \textit{J. V. S. Morales} et al., Colloq. Math. 162, No. 1, 1--22 (2020; Zbl 1457.46067) Full Text: DOI arXiv
Fevrier, Maxime; Mastnak, Mitja; Nica, Alexandru; Szpojankowski, Kamil Using Boolean cumulants to study multiplication and anti-commutators of free random variables. (English) Zbl 1462.46073 Trans. Am. Math. Soc. 373, No. 10, 7167-7205 (2020). MSC: 46L54 46L53 05A18 60C05 60B20 PDFBibTeX XMLCite \textit{M. Fevrier} et al., Trans. Am. Math. Soc. 373, No. 10, 7167--7205 (2020; Zbl 1462.46073) Full Text: DOI arXiv
Crismale, Vitonofrio; Griseta, Maria Elena; Wysoczański, Janusz Weakly monotone Fock space and monotone convolution of the Wigner law. (English) Zbl 1445.46046 J. Theor. Probab. 33, No. 1, 268-294 (2020). MSC: 46L53 46L54 60B99 05A18 PDFBibTeX XMLCite \textit{V. Crismale} et al., J. Theor. Probab. 33, No. 1, 268--294 (2020; Zbl 1445.46046) Full Text: DOI arXiv
Lenczewski, Romuald Conditionally monotone independence and the associated products of graphs. (English) Zbl 1451.46053 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 22, No. 4, Article ID 1950023, 24 p. (2019). MSC: 46L53 05C76 PDFBibTeX XMLCite \textit{R. Lenczewski}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 22, No. 4, Article ID 1950023, 24 p. (2019; Zbl 1451.46053) Full Text: DOI arXiv
Cho, Ilwoo; Jorgensen, Palle Free probability on \( C^*\)-algebras induced by Hecke algebras over primes. (English) Zbl 1450.46049 Discrete Contin. Dyn. Syst., Ser. S 12, No. 8, 2221-2252 (2019). MSC: 46L54 46L53 46S10 47L55 05E16 11R56 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. Jorgensen}, Discrete Contin. Dyn. Syst., Ser. S 12, No. 8, 2221--2252 (2019; Zbl 1450.46049) Full Text: DOI
Novak, Jonathan A tale of two integrals. (English) Zbl 1427.46045 Notices Am. Math. Soc. 66, No. 10, 1696-1697 (2019). MSC: 46L53 60B20 15B52 05A05 14H70 05A15 05C83 PDFBibTeX XMLCite \textit{J. Novak}, Notices Am. Math. Soc. 66, No. 10, 1696--1697 (2019; Zbl 1427.46045) Full Text: DOI
Schleißinger, Sebastian Loewner’s differential equation and spidernets. (English) Zbl 1462.30047 Complex Anal. Oper. Theory 13, No. 8, 3899-3921 (2019). Reviewer: Dmitri V. Prokhorov (Saratov) MSC: 30C80 30C35 46L53 05C50 PDFBibTeX XMLCite \textit{S. Schleißinger}, Complex Anal. Oper. Theory 13, No. 8, 3899--3921 (2019; Zbl 1462.30047) Full Text: DOI arXiv
Matysiak, Wojciech; Świeca, Marcin Multiplicity free actions, birth and death processes on partitions, and Biane’s quantum Ornstein-Uhlenbeck semigroups. arXiv:1905.12263 Preprint, arXiv:1905.12263 [math.PR] (2019). MSC: 60J25 46L53 05A10 22E30 BibTeX Cite \textit{W. Matysiak} and \textit{M. Świeca}, ``Multiplicity free actions, birth and death processes on partitions, and Biane's quantum Ornstein-Uhlenbeck semigroups'', Preprint, arXiv:1905.12263 [math.PR] (2019) Full Text: arXiv OA License
Cho, Ilwoo; Jorgensen, Palle E. T. Analysis of free products of the general linear groups \(\mathrm{GL}_{2}(\mathbb{Q}_{p})\) and Hecke algebras \(\mathcal{H}( \mathrm{GL}_{2}(\mathbb{Q}_{p})) \) over primes \(p\). (English) Zbl 1443.20040 Christensen, Jens Gerlach (ed.) et al., Representation theory and harmonic analysis on symmetric spaces. AMS special session on harmonic analysis, in honor of Gestur Ólafsson’s 65th birthday, Atlanta, GA, USA, January 4, 2017. Proceedings. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 714, 23-75 (2018). MSC: 20E06 20C08 46L54 46L40 46L53 47L55 05E16 20G15 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. E. T. Jorgensen}, Contemp. Math. 714, 23--75 (2018; Zbl 1443.20040) Full Text: DOI
Dahlqvist, Antoine Integration formulas for Brownian motion on classical compact Lie groups. (English. French summary) Zbl 1388.58022 Ann. Inst. Henri Poincaré, Probab. Stat. 53, No. 4, 1971-1990 (2017). Reviewer: Jacques Franchi (Strasbourg) MSC: 58J65 60J65 15A72 14L35 46L53 60H30 60G15 05E10 PDFBibTeX XMLCite \textit{A. Dahlqvist}, Ann. Inst. Henri Poincaré, Probab. Stat. 53, No. 4, 1971--1990 (2017; Zbl 1388.58022) Full Text: DOI arXiv Euclid
Cho, Ilwoo Matrices induced by arithmetic functions acting on certain Krein spaces. (English) Zbl 1380.05197 Spec. Matrices 5, 258-289 (2017). MSC: 05E15 11G15 11R04 11R09 11R47 11R56 46L10 46L40 46L53 46L54 47L15 47L30 47L55 PDFBibTeX XMLCite \textit{I. Cho}, Spec. Matrices 5, 258--289 (2017; Zbl 1380.05197) Full Text: DOI
Cho, Ilwoo; Jorgensen, Palle E. T. Krein-space operators determined by free product algebras induced by primes and graphs. (English) Zbl 1358.05309 Spec. Matrices 5, 1-35 (2017). MSC: 05E15 11G15 11R04 11R09 11R47 11R56 46L10 46L40 46L53 46L54 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. E. T. Jorgensen}, Spec. Matrices 5, 1--35 (2017; Zbl 1358.05309) Full Text: DOI
Obata, Nobuaki Spectral analysis of growing graphs. A quantum probability point of view. (English) Zbl 1366.81005 SpringerBriefs in Mathematical Physics 20. Singapore: Springer (ISBN 978-981-10-3505-0/pbk; 978-981-10-3506-7/ebook). viii, 138 p. (2017). Reviewer: Uwe Franz (Besançon) MSC: 81-02 05-02 05C50 05C76 60F05 46L53 81S25 PDFBibTeX XMLCite \textit{N. Obata}, Spectral analysis of growing graphs. A quantum probability point of view. Singapore: Springer (2017; Zbl 1366.81005) Full Text: DOI
Gerhold, Malte Bimonotone Brownian Motion. arXiv:1708.03510 Preprint, arXiv:1708.03510 [math.OA] (2017). MSC: 46L53 60G51 60F05 05A18 BibTeX Cite \textit{M. Gerhold}, ``Bimonotone Brownian Motion'', Preprint, arXiv:1708.03510 [math.OA] (2017) Full Text: DOI arXiv OA License
Del Moral, Pierre; Bishop, Adrian N. Matrix product moments in normal variables. arXiv:1703.00353 Preprint, arXiv:1703.00353 [math.ST] (2017). MSC: 15B52 60B20 46L53 05A10 BibTeX Cite \textit{P. Del Moral} and \textit{A. N. Bishop}, ``Matrix product moments in normal variables'', Preprint, arXiv:1703.00353 [math.ST] (2017) Full Text: arXiv OA License
Cho, Ilwoo Factorization of \(\mathbb C\)-valued functions induced by graphs. (English) Zbl 1353.05125 Complex Anal. Oper. Theory 10, No. 7, 1453-1499 (2016). MSC: 05E15 05C20 11G15 11R04 11R09 11R47 11R56 46L10 46L40 46L53 46L54 PDFBibTeX XMLCite \textit{I. Cho}, Complex Anal. Oper. Theory 10, No. 7, 1453--1499 (2016; Zbl 1353.05125) Full Text: DOI
Cho, Ilwoo Representations and corresponding operators induced by Hecke algebras. (English) Zbl 1332.05152 Complex Anal. Oper. Theory 10, No. 3, 437-477 (2016). MSC: 05E15 05E10 11G15 11R04 11R09 11R47 11R56 46L10 46L40 46L53 46L54 47L15 47L30 47L55 PDFBibTeX XMLCite \textit{I. Cho}, Complex Anal. Oper. Theory 10, No. 3, 437--477 (2016; Zbl 1332.05152) Full Text: DOI
Ardila, Federico; Rincón, Felipe; Williams, Lauren Positroids and non-crossing partitions. (English) Zbl 1325.05015 Trans. Am. Math. Soc. 368, No. 1, 337-363 (2016). MSC: 05A15 05A17 05B35 14M15 14P10 46L53 PDFBibTeX XMLCite \textit{F. Ardila} et al., Trans. Am. Math. Soc. 368, No. 1, 337--363 (2016; Zbl 1325.05015) Full Text: DOI arXiv
Cho, Ilwoo; Gillespie, Timothy L. Free probability on Hecke algebras. (English) Zbl 1325.11127 Complex Anal. Oper. Theory 9, No. 7, 1491-1531 (2015). MSC: 46L54 05E15 46L10 46L40 46L53 47L55 47S10 PDFBibTeX XMLCite \textit{I. Cho} and \textit{T. L. Gillespie}, Complex Anal. Oper. Theory 9, No. 7, 1491--1531 (2015; Zbl 1325.11127) Full Text: DOI
Cho, Ilwoo; Jorgensen, Palle E. T. Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs. (English) Zbl 1319.05150 Spec. Matrices 3, 123-154 (2015). MSC: 05E18 05E15 05C20 11G15 11R04 11R09 11R47 11R56 46L10 46L40 46L53 46L54 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. E. T. Jorgensen}, Spec. Matrices 3, 123--154 (2015; Zbl 1319.05150) Full Text: DOI
Arizmendi, Octavio; Hasebe, Takahiro; Lehner, Franz; Vargas, Carlos Relations between cumulants in noncommutative probability. (English) Zbl 1319.05019 Adv. Math. 282, 56-92 (2015). MSC: 05A18 46L53 PDFBibTeX XMLCite \textit{O. Arizmendi} et al., Adv. Math. 282, 56--92 (2015; Zbl 1319.05019) Full Text: DOI arXiv
Cho, Ilwoo \(\mathbb C\)-valued functions induced by graphs. (English) Zbl 1314.05228 Complex Anal. Oper. Theory 9, No. 3, 519-565 (2015). MSC: 05E15 11G15 11R04 11R09 11R47 11R56 46L10 46L40 46L53 46L54 PDFBibTeX XMLCite \textit{I. Cho}, Complex Anal. Oper. Theory 9, No. 3, 519--565 (2015; Zbl 1314.05228) Full Text: DOI
Cho, Ilwoo; Jorgensen, Palle E. T. Krein-space representations of arithmetic functions determined by primes. (English) Zbl 1305.05233 Algebr. Represent. Theory 17, No. 6, 1809-1841 (2014). MSC: 05E15 05E10 11G15 11R04 11R09 11R47 11R56 46L10 46L40 46L53 46L54 47L15 47L30 47L55 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. E. T. Jorgensen}, Algebr. Represent. Theory 17, No. 6, 1809--1841 (2014; Zbl 1305.05233) Full Text: DOI
Cho, Ilwoo; Jorgensen, Palle Actions of arithmetic functions on matrices and corresponding representations. (English) Zbl 1309.46037 Ann. Funct. Anal. 5, No. 2, 90-117 (2014). MSC: 46L53 46L54 47L15 47L30 47L55 05E15 46L10 46L40 11N99 PDFBibTeX XMLCite \textit{I. Cho} and \textit{P. Jorgensen}, Ann. Funct. Anal. 5, No. 2, 90--117 (2014; Zbl 1309.46037) Full Text: DOI EMIS
Cho, Ilwoo Free distributional data of arithmetic functions and corresponding generating functions determined by gaps between primes. (English) Zbl 1332.46065 Complex Anal. Oper. Theory 8, No. 2, 537-570 (2014). MSC: 46L54 05E15 11R56 46L10 46L40 46L53 47L15 47L30 47L55 PDFBibTeX XMLCite \textit{I. Cho}, Complex Anal. Oper. Theory 8, No. 2, 537--570 (2014; Zbl 1332.46065) Full Text: DOI
Kula, Anna; Wysoczański, Janusz An example of a Boolean-free type central limit theorem. (English) Zbl 1285.60019 Probab. Math. Stat. 33, No. 2, 341-352 (2013). Reviewer: Allan Gut (Uppsala) MSC: 60F05 60B12 05A18 06A07 46L53 PDFBibTeX XMLCite \textit{A. Kula} and \textit{J. Wysoczański}, Probab. Math. Stat. 33, No. 2, 341--352 (2013; Zbl 1285.60019) Full Text: Link
Lee, Hun Hee; Obata, Nobuaki Distance-\(k\) graphs of hypercube and \(q\)-Hermite polynomials. (English) Zbl 1275.46051 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 16, No. 2, Article ID 1350011, 12 p. (2013). MSC: 46L53 05C50 PDFBibTeX XMLCite \textit{H. H. Lee} and \textit{N. Obata}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 16, No. 2, Article ID 1350011, 12 p. (2013; Zbl 1275.46051) Full Text: DOI arXiv
Banerjee, Sayan; Bose, Arup Noncrossing partitions, Catalan words, and the semicircle law. (English) Zbl 1279.60011 J. Theor. Probab. 26, No. 2, 386-409 (2013). Reviewer: Zakhar Kabluchko (Ulm) MSC: 60B20 60B10 46L53 46L54 05A18 PDFBibTeX XMLCite \textit{S. Banerjee} and \textit{A. Bose}, J. Theor. Probab. 26, No. 2, 386--409 (2013; Zbl 1279.60011) Full Text: DOI
Cho, Ilwoo Operators induced by prime numbers. (English) Zbl 1332.46064 Methods Appl. Anal. 19, No. 4, 313-340 (2012). MSC: 46L54 05E15 11R56 46L10 46L40 46L53 47L15 47L30 47L55 PDFBibTeX XMLCite \textit{I. Cho}, Methods Appl. Anal. 19, No. 4, 313--340 (2012; Zbl 1332.46064) Full Text: DOI
Obata, Nobuaki Asymptotic spectral distributions of distance \(\mathbf k\)-graphs of large-dimensional hypercubes. (English) Zbl 1248.05114 Bożejko, Marek (ed.) et al., Noncommutative harmonic analysis with applications to probability. III: Papers presented at the 13th workshop, Bȩdlewo, Poland, July 11–17, 2010. Warszawa: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-15-7/pbk). Banach Center Publications 96, 287-292 (2012). MSC: 05C50 05C65 05C12 05E30 33C45 46L53 60F05 PDFBibTeX XMLCite \textit{N. Obata}, Banach Cent. Publ. 96, 287--292 (2012; Zbl 1248.05114) Full Text: DOI
Hasebe, Takahiro; Saigo, Hayato Joint cumulants for natural independence. (English) Zbl 1247.46052 Electron. Commun. Probab. 16, 491-506 (2011). MSC: 46L53 46L54 05A18 PDFBibTeX XMLCite \textit{T. Hasebe} and \textit{H. Saigo}, Electron. Commun. Probab. 16, 491--506 (2011; Zbl 1247.46052) Full Text: DOI arXiv
Popa, Mihai; Wang, Jiun-Chau On multiplicative conditionally free convolution. (English) Zbl 1233.46007 Trans. Am. Math. Soc. 363, No. 12, 6309-6335 (2011). MSC: 46L54 46L53 05A18 60E07 PDFBibTeX XMLCite \textit{M. Popa} and \textit{J.-C. Wang}, Trans. Am. Math. Soc. 363, No. 12, 6309--6335 (2011; Zbl 1233.46007) Full Text: DOI arXiv
Kurihara, Jun; Hibino, Yuji Asymptotic spectral analysis of a generalized \(n\)-cube by a quantum probabilistic method. (English) Zbl 1228.05207 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 14, No. 3, 409-417 (2011). MSC: 05C50 46L53 60F05 PDFBibTeX XMLCite \textit{J. Kurihara} and \textit{Y. Hibino}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 14, No. 3, 409--417 (2011; Zbl 1228.05207) Full Text: DOI
Kula, Anna Convolutions related to \(q\)-deformed commutativity. (English) Zbl 1210.28018 Bożejko, Marek (ed.) et al., Noncommutative harmonic analysis with applications to probability. II: Papers presented at the 11th workshop, Bȩdlewo, Poland, August 17–23, 2008. Warszawa: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-08-9/pbk). Banach Center Publications 89, 189-200 (2010). MSC: 28D05 46L53 05A30 42A85 PDFBibTeX XMLCite \textit{A. Kula}, Banach Cent. Publ. 89, 189--200 (2010; Zbl 1210.28018) Full Text: DOI
Kula, Anna The \(q\)-deformed convolutions: examples and applications to moment problem. (English) Zbl 1206.28022 Oper. Matrices 4, No. 4, 593-603 (2010). MSC: 28D05 44A60 05A30 42A85 46L53 PDFBibTeX XMLCite \textit{A. Kula}, Oper. Matrices 4, No. 4, 593--603 (2010; Zbl 1206.28022) Full Text: DOI Link
Wysoczański, Janusz bm-independence and bm-central limit theorems associated with symmetric cones. (English) Zbl 1246.46059 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 13, No. 3, 461-488 (2010). MSC: 46L53 60B12 60F05 05A19 05A18 06A07 PDFBibTeX XMLCite \textit{J. Wysoczański}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 13, No. 3, 461--488 (2010; Zbl 1246.46059) Full Text: DOI
Guionnet, Alice; Shlyakhtenko, Dimitri Free diffusions and matrix models with strictly convex interaction. (English) Zbl 1187.46056 Geom. Funct. Anal. 18(2008), No. 6, 1875-1916 (2009). Reviewer: Isamu Dôku (Saitama) MSC: 46L54 46L53 46L37 15B52 05C30 60B20 PDFBibTeX XMLCite \textit{A. Guionnet} and \textit{D. Shlyakhtenko}, Geom. Funct. Anal. 18, No. 6, 1875--1916 (2009; Zbl 1187.46056) Full Text: DOI arXiv
Bożejko, Marek; Bryc, Włodzimierz A quadratic regression problem for two-state algebras with an application to the central limit theorem. (English) Zbl 1183.46062 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 12, No. 2, 231-249 (2009). MSC: 46L54 46L53 60E05 05A18 PDFBibTeX XMLCite \textit{M. Bożejko} and \textit{W. Bryc}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 12, No. 2, 231--249 (2009; Zbl 1183.46062) Full Text: DOI arXiv
Kümmerer, B. Asymptotic behaviour of quantum Markov processes. (English) Zbl 1178.46061 Hilgert, Joachim (ed.) et al., Proceedings of the fourth German-Japanese symposium on infinite dimensional harmonic analysis IV. On the interplay between representation theory, random matrices, special functions, and probability, Tokyo, Japan, September 10–14, 2007. Hackensack, NJ: World Scientific (ISBN 978-981-283-281-8/hbk). 168-183 (2009). Reviewer: Michael Skeide (Campobasso) MSC: 46L53 60J10 46L57 60C05 05C99 PDFBibTeX XMLCite \textit{B. Kümmerer}, in: Proceedings of the fourth German-Japanese symposium on infinite dimensional harmonic analysis IV. On the interplay between representation theory, random matrices, special functions, and probability, Tokyo, Japan, September 10--14, 2007. Hackensack, NJ: World Scientific. 168--183 (2009; Zbl 1178.46061)
Obata, Nobuaki Notions of independence in quantum probability and spectral analysis of graphs. (English) Zbl 1170.46056 Selected papers on analysis and related topics. Transl. from the Japanese by Hidekazu Tanaka. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-3928-7/hbk). Translations. Series 2. American Mathematical Society 223, 115-136 (2008). MSC: 46L53 05C50 46L54 46L60 60C05 81S25 PDFBibTeX XMLCite \textit{N. Obata}, Transl., Ser. 2, Am. Math. Soc. 223, 115--136 (2008; Zbl 1170.46056)
Kula, Anna; Ricard, Éric On the convolution for \(q\)-normal elements. (English) Zbl 1190.05020 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 11, No. 4, 565-588 (2008). MSC: 05A30 46L53 60F05 PDFBibTeX XMLCite \textit{A. Kula} and \textit{É. Ricard}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 11, No. 4, 565--588 (2008; Zbl 1190.05020) Full Text: DOI
Bożejko, Marek Bessis–Moussa–Villani conjecture and generalized Gaussian random variables. (English) Zbl 1165.46305 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 11, No. 3, 313-321 (2008). MSC: 46L53 05A18 PDFBibTeX XMLCite \textit{M. Bożejko}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 11, No. 3, 313--321 (2008; Zbl 1165.46305) Full Text: DOI
Lenczewski, Romuald Operators related to subordination for free multiplicative convolutions. (English) Zbl 1155.46035 Indiana Univ. Math. J. 57, No. 3, 1055-1103 (2008). MSC: 46L54 46L53 05C50 PDFBibTeX XMLCite \textit{R. Lenczewski}, Indiana Univ. Math. J. 57, No. 3, 1055--1103 (2008; Zbl 1155.46035) Full Text: DOI arXiv
Liang, Song; Obata, Nobuaki; Takahashi, Shuji Asymptotic spectral analysis of generalized Erdős-Rényi random graphs. (English) Zbl 1132.05058 Bozejko, Marek (ed.) et al., Noncommutative harmonic analysis with applications to probability. Papers presented at the 9th workshop, Bȩdlewo, Poland, September 29–October 10, 2006. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 78, 211-229 (2008). MSC: 05C80 05C50 46L53 60F05 68R10 94C15 PDFBibTeX XMLCite \textit{S. Liang} et al., Banach Cent. Publ. 78, 211--229 (2008; Zbl 1132.05058)
Hora, Akihito; Obata, Nobuaki Asymptotic spectral analysis of growing regular graphs. (English) Zbl 1134.46042 Trans. Am. Math. Soc. 360, No. 2, 899-923 (2008). MSC: 46L53 05C50 42C05 60F05 81S25 PDFBibTeX XMLCite \textit{A. Hora} and \textit{N. Obata}, Trans. Am. Math. Soc. 360, No. 2, 899--923 (2008; Zbl 1134.46042) Full Text: DOI
Cho, Ilwoo Characterization of amalgamated free blocks of a graph von Neumann algebra. (English) Zbl 1129.46050 Complex Anal. Oper. Theory 1, No. 3, 367-398 (2007). MSC: 46L10 46L53 20L05 05C20 PDFBibTeX XMLCite \textit{I. Cho}, Complex Anal. Oper. Theory 1, No. 3, 367--398 (2007; Zbl 1129.46050) Full Text: DOI
Dykema, Kenneth J. Multilinear function series and transforms in free probability theory. (English) Zbl 1111.46045 Adv. Math. 208, No. 1, 351-407 (2007). Reviewer: Isamu Dôku (Saitama) MSC: 46L54 46L53 16W60 05A05 PDFBibTeX XMLCite \textit{K. J. Dykema}, Adv. Math. 208, No. 1, 351--407 (2007; Zbl 1111.46045) Full Text: DOI arXiv
Krystek, Anna Dorota Remarks on the Boolean convolution and Kerov’s \(\alpha\)-transformation. (English) Zbl 1109.46056 Bożejko, Marek (ed.) et al., Quantum probability. Papers presented at the 25th QP conference on quantum probability and related topics, Będlewo, Poland, June 20–26, 2004. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 73, 285-298 (2006). MSC: 46L53 05E05 60J05 PDFBibTeX XMLCite \textit{A. D. Krystek}, Banach Cent. Publ. 73, 285--298 (2006; Zbl 1109.46056) Full Text: Link
Igarashi, Daisuke; Obata, Nobuaki Asymptotic spectral analysis of growing graphs: odd graphs and spidernets. (English) Zbl 1109.46055 Bożejko, Marek (ed.) et al., Quantum probability. Papers presented at the 25th QP conference on quantum probability and related topics, Będlewo, Poland, June 20–26, 2004. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 73, 245-265 (2006). MSC: 46L53 05C50 60F05 81S25 PDFBibTeX XMLCite \textit{D. Igarashi} and \textit{N. Obata}, Banach Cent. Publ. 73, 245--265 (2006; Zbl 1109.46055) Full Text: Link
Hora, Akihito; Obata, Nobuaki An interacting Fock space with periodic Jacobi parameter obtained from regular graphs in large scale limit. (English) Zbl 1107.46042 Hida, Takeyuki (ed.) et al., Quantum information V. Proceedings of the 5th international conference, Nagoya, Japan, December 17–19, 2001. Hackensack, NJ: World Scientific (ISBN 981-238-585-1/hbk). 121-144 (2006). MSC: 46L53 05C99 PDFBibTeX XMLCite \textit{A. Hora} and \textit{N. Obata}, in: Quantum information V. Proceedings of the 5th international conference, Nagoya, Japan, December 17--19, 2001. Hackensack, NJ: World Scientific. 121--144 (2006; Zbl 1107.46042)
Śniady, Piotr Gaussian fluctuations of characters of symmetric groups and of Young diagrams. (English) Zbl 1104.46035 Probab. Theory Relat. Fields 136, No. 2, 263-297 (2006). MSC: 46L53 46L54 60B15 20P05 05E10 20C30 PDFBibTeX XMLCite \textit{P. Śniady}, Probab. Theory Relat. Fields 136, No. 2, 263--297 (2006; Zbl 1104.46035) Full Text: DOI arXiv
Anshelevich, Michael Linearization coefficients for orthogonal polynomials using stochastic processes. (English) Zbl 1092.05076 Ann. Probab. 33, No. 1, 114-136 (2005). MSC: 05E35 05A18 05A30 46L53 60G51 PDFBibTeX XMLCite \textit{M. Anshelevich}, Ann. Probab. 33, No. 1, 114--136 (2005; Zbl 1092.05076) Full Text: DOI arXiv
Goodman, Frederick M. \(\mathbb{Z}_n\)-graded independence. (English) Zbl 1064.46049 Indiana Univ. Math. J. 53, No. 2, 515-532 (2004). MSC: 46L53 05A18 PDFBibTeX XMLCite \textit{F. M. Goodman}, Indiana Univ. Math. J. 53, No. 2, 515--532 (2004; Zbl 1064.46049) Full Text: DOI arXiv
Lehner, Franz Cumulants in noncommutative probability theory. I: Noncommutative exchangeability systems. (English) Zbl 1089.46040 Math. Z. 248, No. 1, 67-100 (2004). Reviewer: Debashish Goswami (Kolkata) MSC: 46L53 05A18 PDFBibTeX XMLCite \textit{F. Lehner}, Math. Z. 248, No. 1, 67--100 (2004; Zbl 1089.46040) Full Text: DOI arXiv
Hora, Akihito A noncommutative version of Kerov’s Gaussian limit for the Plancherel measure of the symmetric group. (English) Zbl 1031.60004 Vershik, A. M. (ed.), Asymptotic combinatorics with applications to mathematical physics. A European mathematical summer school held at the Euler Institute, St. Petersburg, Russia, July 9-20, 2001. Berlin: Springer. Lect. Notes Math. 1815, 77-88 (2003). Reviewer: Isamu Dôku (Saitama) MSC: 60B12 46L53 47N99 05E10 PDFBibTeX XMLCite \textit{A. Hora}, Lect. Notes Math. 1815, 77--88 (2003; Zbl 1031.60004)
Feinsilver, Philip; Kocik, Jerzy Krawtchouk matrices from classical and quantum random walks. (English) Zbl 1014.60049 Viana, Marlos A. G. (ed.) et al., Algebraic methods in statistics and probability. AMS special session on algebraic methods in statistics, Univ. of Notre Dame, IN, USA, April 8-9, 2000. Providence, RI: AMS, American Mathematical Society. Contemp. Math. 287, 83-96 (2001). MSC: 60G50 05B20 47A80 46L53 PDFBibTeX XMLCite \textit{P. Feinsilver} and \textit{J. Kocik}, Contemp. Math. 287, 83--96 (2001; Zbl 1014.60049) Full Text: arXiv
Anshelevich, Michael Partition-dependent stochastic measures and \(q\)-deformed cumulants. (English) Zbl 1010.46064 Doc. Math. 6, 343-384 (2001). Reviewer: Stanislaw Goldstein (Łodz) MSC: 46L53 60H05 05A18 46L10 60E07 81S05 46L54 PDFBibTeX XMLCite \textit{M. Anshelevich}, Doc. Math. 6, 343--384 (2001; Zbl 1010.46064) Full Text: EuDML EMIS
Młotkowski, Wojciech Free probability on algebras with infinitely many states. (English) Zbl 0941.60020 Probab. Theory Relat. Fields 115, No. 4, 579-596 (1999). MSC: 60B99 46L53 05A18 PDFBibTeX XMLCite \textit{W. Młotkowski}, Probab. Theory Relat. Fields 115, No. 4, 579--596 (1999; Zbl 0941.60020) Full Text: DOI
Biane, Philippe Representations of symmetric groups and free probability. (English) Zbl 0927.20008 Adv. Math. 138, No. 1, 126-181 (1998). Reviewer: Andrej Bulinski (Moskva) MSC: 20C30 46L53 20C32 05E10 60B15 PDFBibTeX XMLCite \textit{P. Biane}, Adv. Math. 138, No. 1, 126--181 (1998; Zbl 0927.20008) Full Text: DOI
Mingo, James A.; Nica, Alexandru Crossings of set-partitions and addition of graded-independent random variables. (English) Zbl 0894.46047 Int. J. Math. 8, No. 5, 645-664 (1997). MSC: 46L51 46L53 46L54 60K40 05A18 PDFBibTeX XMLCite \textit{J. A. Mingo} and \textit{A. Nica}, Int. J. Math. 8, No. 5, 645--664 (1997; Zbl 0894.46047) Full Text: DOI
Goulden, Ian P.; Jackson, David M. Connexion coefficients for the symmetric group, free products in operator algebras and random matrices. (English) Zbl 0889.46052 Voiculescu, Dan-Virgil (ed.), Free probability theory. Papers from a workshop on random matrices and operator algebra free products, Toronto, Canada, Mars 1995. Providence, RI: American Mathematical Society. Fields Inst. Commun. 12, 105-125 (1997). MSC: 46L51 46L53 46L54 05E15 47B80 57M50 81Q30 PDFBibTeX XMLCite \textit{I. P. Goulden} and \textit{D. M. Jackson}, Fields Inst. Commun. 12, 105--125 (1997; Zbl 0889.46052)
Nica, Alexandru; Speicher, Roland A “Fourier transform” for multiplicative functions on non-crossing partitions. (English) Zbl 0872.06005 J. Algebr. Comb. 6, No. 2, 141-160 (1997). Reviewer: R.Speicher (Heidelberg) MSC: 06A07 05A18 46L51 46L53 46L54 PDFBibTeX XMLCite \textit{A. Nica} and \textit{R. Speicher}, J. Algebr. Comb. 6, No. 2, 141--160 (1997; Zbl 0872.06005) Full Text: DOI