Neufeld, Leonie Weighted sums and Berry-Esseen type estimates in free probability theory. (English) Zbl 07938776 Probab. Theory Relat. Fields 190, No. 3-4, 803-879 (2024). MSC: 46L54 60E05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
O’Rourke, Sean; Wood, Philip Matchett Quantitative results for banded Toeplitz matrices subject to random and deterministic perturbations. (English) Zbl 1508.15021 Linear Algebra Appl. 657, 50-126 (2023). Reviewer: Yaogan Mensah (Lomé) MSC: 15B05 15B52 47A55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ben Arous, Gérard; Bourgade, Paul; McKenna, Benjamin Exponential growth of random determinants beyond invariance. (English) Zbl 1511.60013 Probab. Math. Phys. 3, No. 4, 731-789 (2022). Reviewer: Roksana Słowik (Gliwice) MSC: 60B20 15B52 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mckenna, Benjamin Large deviations for extreme eigenvalues of deformed Wigner random matrices. (English) Zbl 1472.60012 Electron. J. Probab. 26, Paper No. 34, 37 p. (2021). Reviewer: Oleg K. Zakusilo (Kyïv) MSC: 60B20 15A18 15B52 60F10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bose, Arup; Bhattacharjee, Madhuchhanda Kernel density estimates in a non-standard situation. (English) Zbl 1458.62087 J. Stat. Theory Pract. 15, No. 1, Paper No. 22, 19 p. (2021). MSC: 62G07 62E20 60E15 60B20 15B52 × Cite Format Result Cite Review PDF Full Text: DOI
Banna, Marwa; Mai, Tobias Hölder continuity of cumulative distribution functions for noncommutative polynomials under finite free Fisher information. (English) Zbl 1460.46057 J. Funct. Anal. 279, No. 8, Article ID 108710, 44 p. (2020). MSC: 46L54 60B10 60B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Guionnet, Alice; Husson, Jonathan Large deviations for the largest eigenvalue of Rademacher matrices. (English) Zbl 1444.60021 Ann. Probab. 48, No. 3, 1436-1465 (2020). MSC: 60F10 60B20 15B52 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Erdős, László; Krüger, Torben; Nemish, Yuriy Local laws for polynomials of Wigner matrices. (English) Zbl 1434.60024 J. Funct. Anal. 278, No. 12, Article ID 108507, 59 p. (2020). MSC: 60B20 46L54 15B52 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Götze, Friedrich; Kösters, Holger Convergence and asymptotic approximations to universal distributions in probability. (English) Zbl 1458.60035 Baake, Michael (ed.) et al., Spectral structures and topological methods in mathematics. Zürich: European Mathematical Society (EMS). EMS Ser. Congr. Rep., 1-28 (2019). MSC: 60F05 60E05 × 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
Cook, Nicholas; Hachem, Walid; Najim, Jamal; Renfrew, David Non-Hermitian random matrices with a variance profile. I: Deterministic equivalents and limiting esds. (English) Zbl 1401.60008 Electron. J. Probab. 23, Paper No. 110, 61 p. (2018). MSC: 60B20 15B52 15A18 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Yang, Lifang; Hu, Jiang Kernel estimators for Marčenko-Pastur law of quaternion sample covariance matrices. (English) Zbl 1379.60007 Stat. Probab. Lett. 126, 230-237 (2017). MSC: 60B20 60B10 62G07 × Cite Format Result Cite Review PDF Full Text: DOI
Bun, Joël; Bouchaud, Jean-Philippe; Potters, Marc Cleaning large correlation matrices: tools from random matrix theory. (English) Zbl 1359.15031 Phys. Rep. 666, 1-109 (2017). MSC: 15B52 62G05 91G10 62P05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Edelman, Alan; Guionnet, A.; Péché, S. Beyond universality in random matrix theory. (English) Zbl 1408.60007 Ann. Appl. Probab. 26, No. 3, 1659-1697 (2016). MSC: 60B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Götze, F.; Tikhomirov, A. Optimal bounds for convergence of expected spectral distributions to the semi-circular law. (English) Zbl 1338.60014 Probab. Theory Relat. Fields 165, No. 1-2, 163-233 (2016). MSC: 60B20 60F99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wang, Chen; Jin, Baisuo; Bai, Z. D.; Nair, K. Krishnan; Harding, Matthew Strong limit of the extreme eigenvalues of a symmetrized auto-cross covariance matrix. (English) Zbl 1328.60088 Ann. Appl. Probab. 25, No. 6, 3624-3683 (2015). MSC: 60F15 60B20 15B52 15A18 60F05 60F17 62H25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Chen, Binbin; Pan, Guangming CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size. (English) Zbl 1385.60044 Bernoulli 21, No. 2, 1089-1133 (2015). MSC: 60F05 62H15 60B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Li, Huiqin; Bai, Zhidong Convergence rates of spectral distributions of large dimensional quaternion sample covariance matrices. (English) Zbl 1312.15052 J. Korean Stat. Soc. 44, No. 1, 28-44 (2015). MSC: 15B52 62E20 60F15 60F17 × 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
Paul, Debashis; Aue, Alexander Random matrix theory in statistics: a review. (English) Zbl 1287.62011 J. Stat. Plann. Inference 150, 1-29 (2014). MSC: 62H99 15B52 62H05 × Cite Format Result Cite Review PDF Full Text: DOI Link
Xia, Ningning; Qin, Yingli; Bai, Zhidong Convergence rates of eigenvector empirical spectral distribution of large dimensional sample covariance matrix. (English) Zbl 1285.15018 Ann. Stat. 41, No. 5, 2572-2607 (2013). Reviewer: Costică Moroşanu (Iaşi) MSC: 15B52 15A18 60F15 62E20 60F17 62J10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Anderson, Greg W. Convergence of the largest singular value of a polynomial in independent Wigner matrices. (English) Zbl 1282.60007 Ann. Probab. 41, No. 3B, 2103-2181 (2013). Reviewer: Zakhar Kabluchko (Ulm) MSC: 60B20 15B52 46L54 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Kargin, Vladislav A concentration inequality and a local law for the sum of two random matrices. (English) Zbl 1260.60015 Probab. Theory Relat. Fields 154, No. 3-4, 677-702 (2012). MSC: 60B20 60B10 46L54 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dumitriu, Ioana; Pal, Soumik Sparse regular random graphs: spectral density and eigenvectors. (English) Zbl 1255.05173 Ann. Probab. 40, No. 5, 2197-2235 (2012). MSC: 05C80 05C42 60B20 60C05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Bhamidi, Shankar; Evans, Steven N.; Sen, Arnab Spectra of large random trees. (English) Zbl 1255.05114 J. Theor. Probab. 25, No. 3, 613-654 (2012). Reviewer: Yilun Shang (Shanghai) MSC: 05C50 05C80 60C05 60B20 60J80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Speicher, Roland; Vargas, Carlos [Mai, Tobias] Free deterministic equivalents, rectangular random matrix models, and operator-valued free probability theory. (English) Zbl 1263.46053 Random Matrices Theory Appl. 1, No. 2, 1150008, 26 p. (2012). Reviewer: Stephen Curran (Los Angeles) MSC: 46L54 60B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Johansson, Kurt Universality for certain Hermitian Wigner matrices under weak moment conditions. (English. French summary) Zbl 1279.60014 Ann. Inst. Henri Poincaré, Probab. Stat. 48, No. 1, 47-79 (2012). MSC: 60B20 15B52 82B44 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Bai, Zhidong; Hu, Jiang; Zhou, Wang Convergence rates to the Marchenko-Pastur type distribution. (English) Zbl 1234.60033 Stochastic Processes Appl. 122, No. 1, 68-92 (2012). MSC: 60F15 62H99 × Cite Format Result Cite Review PDF Full Text: DOI
Bobkov, S. G.; Götze, F.; Tikhomirov, A. N. On concentration of empirical measures and convergence to the semi-circle law. (English) Zbl 1247.60010 J. Theor. Probab. 23, No. 3, 792-823 (2010). Reviewer: Michael Voit (Dortmund) MSC: 60B20 × Cite Format Result Cite Review PDF Full Text: DOI
Tao, Terence; Vu, Van Random matrices: The distribution of the smallest singular values. (English) Zbl 1210.60014 Geom. Funct. Anal. 20, No. 1, 260-297 (2010). Reviewer: Martín Argerami (Regina) MSC: 60B20 15B52 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bobkov, S. G.; Götze, F.; Tikhomirov, A. N. On concentration of high-dimensional matrices with randomly signed entries. (English) Zbl 1288.60004 J. Math. Sci., New York 163, No. 4, 328-351 (2009) and Zap. Nauchn. Semin. POMI 364, 32-69 (2009). MSC: 60B20 60E10 60F05 × Cite Format Result Cite Review PDF Full Text: DOI
Erdős, László; Schlein, Benjamin; Yau, Horng-Tzer Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices. (English) Zbl 1175.15028 Ann. Probab. 37, No. 3, 815-852 (2009). Reviewer: Yueh-er Kuo (Knoxville) MSC: 15B52 82B44 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Götze, Friedrich; Tikhomirov, Alexander N.; Timushev, Dmitry A. Rate of convergence to the semi-circle law for the deformed Gaussian unitary Ensemble. (English) Zbl 1155.15027 Cent. Eur. J. Math. 5, No. 2, 305-334 (2007). Reviewer: Costică Moroşanu (Iaşi) MSC: 15B52 60F99 41A60 × Cite Format Result Cite Review PDF Full Text: DOI
Kargin, Vladislav Berry–Esseen for free random variables. (English) Zbl 1124.46049 J. Theor. Probab. 20, No. 2, 381-395 (2007). MSC: 46L54 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ruzmaikina, A. Universality of the edge distribution of eigenvalues of Wigner random matrices with polynomially decaying distributions of entries. (English) Zbl 1130.82313 Commun. Math. Phys. 261, No. 2, 277-296 (2006). MSC: 82B44 15B52 82B41 60F99 × Cite Format Result Cite Review PDF Full Text: DOI
Bai, Z. D.; Yao, J. On the convergence of the spectral empirical process of Wigner matrices. (English) Zbl 1101.60012 Bernoulli 11, No. 6, 1059-1092 (2005). MSC: 60F05 15B57 82B31 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Götze, Friedrich; Tikhomirov, Alexander The rate of convergence for spectra of GUE and LUE matrix ensembles. (English) Zbl 1108.60014 Cent. Eur. J. Math. 3, No. 4, 666-704 (2005). MSC: 60F05 15B52 33C45 82B31 × Cite Format Result Cite Review PDF Full Text: DOI
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
Götze, Friedrich; Tikhomirov, Alexander Rate of convergence in probability to the Marchenko-Pastur law. (English) Zbl 1049.60018 Bernoulli 10, No. 3, 503-548 (2004). MSC: 60F05 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Ledoit, Olivier; Wolf, Michael Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size. (English) Zbl 1029.62049 Ann. Stat. 30, No. 4, 1081-1102 (2002). MSC: 62H15 62E20 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Sinajĭ, Ya. G.; Soshnikov, A. B. A refinement of Wigner’s semicircle law in a neighborhood of the spectrum edge for random symmetric matrices. (English. Russian original) Zbl 0930.15025 Funct. Anal. Appl. 32, No. 2, 114-131 (1998); translation from Funkts. Anal. Prilozh. 32, No. 2, 56-79 (1998). Reviewer: Alexei Khorunzhy (Khar’kov) MSC: 15B52 60F05 15A18 × 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
Bai, Z. D. Circular law. (English) Zbl 0871.62018 Ann. Probab. 25, No. 1, 494-529 (1997). Reviewer: N.G.Gamkrelidze (Moskva) MSC: 62E20 60F15 62H99 62E10 62H05 × Cite Format Result Cite Review PDF Full Text: DOI