Cho, Ilwoo On free random variables followed by the semicircular law. (English) Zbl 07971181 Pure Appl. Funct. Anal. 9, No. 6, 1547-1581 (2024). MSC: 46L54 46H35 47A45 × Cite Format Result Cite Review PDF Full Text: Link
Cho, Ilwoo; Jorgensen, Palle E. T. Free random variables whose free distributions are dictated by the semicircular law. (English) Zbl 07919752 Adv. Oper. Theory 9, No. 2, Paper No. 34, 39 p. (2024). MSC: 46L54 47L55 × Cite Format Result Cite Review PDF Full Text: DOI
Cho, Ilwoo; Dong, Junyi Catalan numbers and free distributions of mutually free multi semicircular elements. (English) Zbl 1548.46050 Complex Anal. Oper. Theory 18, No. 2, Paper No. 23, 46 p. (2024). MSC: 46L54 46L10 11B83 47L55 × Cite Format Result Cite Review PDF Full Text: DOI
Ma, Yu Tao Unified limits and large deviation principles for \(\beta\)-Laguerre ensembles in global regime. (English) Zbl 1522.60039 Acta Math. Sin., Engl. Ser. 39, No. 7, 1271-1288 (2023). MSC: 60F10 15B52 × Cite Format Result Cite Review PDF Full Text: DOI
Cho, Ilwoo; Dutta, Hemen Spectral properties of certain operators on a free Hilbert space and the semicircular law. (English) Zbl 1533.47002 Amsterdam: Elsevier/Academic Press (ISBN 978-0-443-15175-0/pbk; 978-0-443-15176-7/ebook). x, 154 p. (2023). Reviewer: Ali Talebi (Mashhad) MSC: 47-02 46-02 47C15 46L54 × Cite Format Result Cite Review PDF Full Text: DOI
Cho, Ilwoo; Jorgensen, Palle Comparing Banach spaces for systems of free random variables followed by the semicircular law. (English) Zbl 1545.46051 Aron, Richard M. (ed.) et al., Operator and norm inequalities and related topics. Cham: Birkhäuser. Trends Math., 773-822 (2022). MSC: 46L54 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI
Cho, Ilwoo; Jorgensen, Palle E. T. Certain \(*\)-homomorphisms of \(C^*\)-algebras and sequences of semicircular elements: a Banach space view. (English) Zbl 1465.46065 Ill. J. Math. 64, No. 4, 519-567 (2020). MSC: 46L54 46L10 47L55 47L65 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Cébron, Guillaume; Fathi, Max; Mai, Tobias A note on existence of free Stein kernels. (English) Zbl 1446.46045 Proc. Am. Math. Soc. 148, No. 4, 1583-1594 (2020). MSC: 46L54 60F05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Cho, Ilwoo Asymptotic semicircular law induced by \(p\)-adic number fields \(\mathbb{Q}_p\) over primes. (English) Zbl 1428.11102 Complex Anal. Oper. Theory 13, No. 7, 3169-3206 (2019). MSC: 11F85 11G15 11R47 11R56 46L10 46L54 47L30 47L55 × Cite Format Result Cite Review PDF Full Text: DOI
Xia, Ningning; Bai, Zhidong Convergence rate of eigenvector empirical spectral distribution of large Wigner matrices. (English) Zbl 1420.62235 Stat. Pap. 60, No. 3, 633-665 (2019). Reviewer: Fraser Daly (Edinburgh) MSC: 62H10 60F05 60B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Shang, Yilun On the skew-spectral distribution of randomly oriented graphs. (English) Zbl 1499.05582 Ars Comb. 140, 63-71 (2018). MSC: 05C80 60B20 15A18 60C05 05C50 × Cite Format Result Cite Review PDF Full Text: arXiv
Józiak, Paweł; Szpojankowski, Kamil Quantum Bernstein’s theorem and the hyperoctahedral quantum group. (English) Zbl 1398.81130 J. Math. Phys. 59, No. 6, 063511, 10 p. (2018). Reviewer: Simeng Wang (Saarbrücken) MSC: 81R50 46L53 17B37 46L54 46L65 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Yin, Yanqing; Bai, Zhidong; Hu, Jiang On the semicircular law of large-dimensional random quaternion matrices. (English) Zbl 1353.60024 J. Theor. Probab. 29, No. 3, 1100-1120 (2016). MSC: 60F05 60B20 60F15 62E20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Jana, I.; Saha, K.; Soshnikov, A. Fluctuations of linear eigenvalue statistics of random band matrices. (English) Zbl 1348.15024 Theory Probab. Appl. 60, No. 3, 407-443 (2016) and Teor. Veroyatn. Primen. 60, No. 3, 553-592 (2016). MSC: 15B52 15A18 60B20 60F05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Yin, Yanqing; Bai, Zhidong Convergence rates of the spectral distributions of large random quaternion self-dual Hermitian matrices. (English) Zbl 1309.15055 J. Stat. Phys. 157, No. 6, 1207-1224 (2014). Reviewer: A. Arvanitoyeorgos (Patras) MSC: 15B52 60F15 62E20 60F17 60B20 15A18 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Nourdin, Ivan; Peccati, Giovanni; Speicher, Roland Multi-dimensional semicircular limits on the free Wigner chaos. (English) Zbl 1295.46046 Dalang, Robert C. (ed.) et al., Seminar on stochastic analysis, random fields and applications VII. Centro Stefano Franscini, Ascona (Ticino), Switzerland, May 23–27, 2011. Basel: Birkhäuser/Springer (ISBN 978-3-0348-0544-5/hbk; 978-3-0348-0545-2/ebook). Progress in Probability 67, 211-221 (2013). Reviewer: Isamu Dôku (Saitama) MSC: 46L54 60H05 60H07 60H30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Basu, Riddhipratim; Bose, Arup; Ganguly, Shirshendu; Hazra, Rajat Subhra Spectral properties of random triangular matrices. (English) Zbl 1258.60010 Random Matrices Theory Appl. 1, No. 3, 1250003, 22 p. (2012). Reviewer: Martín Argerami (Regina) MSC: 60B20 46L54 15B52 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Tao, Terence Topics in random matrix theory. (English) Zbl 1256.15020 Graduate Studies in Mathematics 132. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-7430-1/hbk). x, 282 p. (2012). Reviewer: Xiangqian Guo (Waterloo) MSC: 15B52 60B20 15B35 15-02 15B57 15A18 15A60 × Cite Format Result Cite Review PDF
Bai, Z. D.; Pan, G. M. Limiting behavior of eigenvectors of large Wigner matrices. (English) Zbl 1235.82035 J. Stat. Phys. 146, No. 3, 519-549 (2012). MSC: 82B44 15B52 60F05 × Cite Format Result Cite Review PDF Full Text: DOI
Bose, Arup; Hazra, Rajat Subhra; Saha, Koushik Half independence and half cumulants. (English) Zbl 1246.60013 Electron. Commun. Probab. 16, 405-422 (2011). MSC: 60B20 46L53 46L54 60B10 × Cite Format Result Cite Review PDF Full Text: DOI
Bai, Zhidong; Hu, Jiang; Pan, Guangming; Zhou, Wang A note on rate of convergence in probability to semicircular law. (English) Zbl 1244.60022 Electron. J. Probab. 16, Paper No. 88, 2439-2451 (2011). MSC: 60F05 60B20 62H99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bai, Z. D.; Liu, H. X.; Wong, W. K. Asymptotic properties of eigenmatrices of a large sample covariance matrix. (English) Zbl 1234.15013 Ann. Appl. Probab. 21, No. 5, 1994-2015 (2011). Reviewer: Grozio Stanilov (Sofia) MSC: 15B52 60F05 15A18 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bose, Arup; Hazra, Rajat Subhra; Saha, Koushik Convergence of joint moments for independent random patterned matrices. (English) Zbl 1231.60006 Ann. Probab. 39, No. 4, 1607-1620 (2011). Reviewer: Michael Stolz (Bochum) MSC: 60B20 60B10 46L54 15B05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bose, Arup; Sen, Arnab Another look at the moment method for large dimensional random matrices. (English) Zbl 1190.60013 Electron. J. Probab. 13, 588-628 (2008). MSC: 60F05 60F15 62E20 60G57 60B20 82B31 × Cite Format Result Cite Review PDF Full Text: DOI EuDML EMIS
Chatterjee, S.; Bose, A. A new method for bounding rates of convergence of empirical spectral distributions. (English) Zbl 1063.60024 J. Theor. Probab. 17, No. 4, 1003-1019 (2004). MSC: 60F05 × Cite Format Result Cite Review PDF Full Text: DOI
Bai, Z. D.; Miao, Baiqi; Tsay, Jhishen Convergence rates of the spectral distributions of large Wigner matrices. (English) Zbl 0987.60050 Int. Math. J. 1, No. 1, 65-90 (2002). MSC: 60F99 60B10 × Cite Format Result Cite Review PDF
Bai, Z. D.; Miao, Baiqi; Tsay, Jhishen Remarks on the convergence rate of the spectral distributions of Wigner matrices. (English) Zbl 0928.60007 J. Theor. Probab. 12, No. 2, 301-311 (1999). MSC: 60F05 62E20 × Cite Format Result Cite Review PDF Full Text: DOI
Bai, Z. D.; Miao, Baiqi; Tsay, Jhishen A note on the convergence rate of the spectral distributions of large random matrices. (English) Zbl 0894.60034 Stat. Probab. Lett. 34, No. 1, 95-101 (1997). MSC: 60F99 × Cite Format Result Cite Review PDF Full Text: DOI
Girko, V. L. A matrix equation for resolvents of random matrices with independent blocks. (English. Russian original) Zbl 0858.15009 Theory Probab. Appl. 40, No. 4, 635-644 (1995); translation from Teor. Veroyatn. Primen. 40, No. 4, 741-753 (1995). Reviewer: Eugene Seneta (Sydney) MSC: 15B52 15A24 × Cite Format Result Cite Review PDF
Sommer, Jens-Uwe; Trautenberg, Hans L. The eigenvalue spectrum of a large symmetric random matrix with exponential distributed elements. (English) Zbl 0814.15007 J. Phys. A, Math. Gen. 26, No. 17, 4419-4429 (1993). Reviewer: V.Burjan (Praha) MSC: 15A18 15A42 15B52 65F15 × Cite Format Result Cite Review PDF Full Text: DOI
Bai, Z. D. Convergence rate of expected spectral distributions of large random matrices. I: Wigner matrices. (English) Zbl 0779.60024 Ann. Probab. 21, No. 2, 625-648 (1993). Reviewer: V.Sakalauskas (Kaunas) MSC: 60F15 62F15 × Cite Format Result Cite Review PDF Full Text: DOI
Girko, V. L. Elliptic law and elements of G-analysis. (English) Zbl 0647.60032 Probability theory and mathematical statistics, Proc. 4th Conf., Vilnius/USSR 1985, Vol. 1, 489-507 (1987). Reviewer: Lin Zhengyan MSC: 60F15 60F05 × Cite Format Result Cite Review PDF
Girko, V. L. Elliptic law. (English. Russian original) Zbl 0658.62023 Theory Probab. Appl. 30, 677-690 (1986); translation from Teor Veroyatn. Primen. 30, No. 4, 640-651 (1985). MSC: 62E20 60F15 15B52 60F99 × Cite Format Result Cite Review PDF Full Text: DOI
Majumdar, C. K. Random matrices in condensed matter physics. (English) Zbl 0525.15014 Stochastic processes - formalism and applications, Proc. Winter Sch., Hyderabad/India 1982, Lect. Notes Phys. 184, 286-299 (1983). MSC: 15B52 15B51 82D20 × Cite Format Result Cite Review PDF