[1] Anderson T.An Introduction to Multivariate Statistical Analysis. New Jersey: John Wiley & Sons, 1984
[2] Bakry D, Gentil I, Ledoux M.Analysis and Geometry of Markov Diffusion Operators. Cham: Springer, 2014
[3] Baik J, Deift P, Johansson K. On the distribution of the length of the longest increasing subsequence of random permutations. J Amer Math Soc, 1999, 12(4): 1119-1178
[4] Bobkov S G, Ledoux M. From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities. Geom Funct Anal, 2010, 10(5): 1028-1052
[5] Cai M, Lei L, Ma Y. Approximation of β-Laguerre ensembles by β-Hermite ensembles. J Math (Chinese), 2022, 42(5): 437-444
[6] Chafai D, Lehec J.On Poincaré and logarithmic Sobolev inequalities for a class of singular Gibbs measures//Klartag B, Milman E. Geometric Aspects Functional Analysis. Cham: Springer, 2020
[7] Dumitriu I, Edelman A. Matrix models for beta ensembles. J Math Phys, 2002, 43(11): 5830-5847
[8] Edelman A. Eigenvalues and condition numbers of random matrices. SIAM J Matrix Anal Appl, 1988, 9: 543-560
[9] Edelman A, Sutton B. The beta-Jacobi matrix model, the CS decomposition,generalized singular value problems. Found Comput Math, 2008, 8(2): 259-285
[10] Fisher R A. On the mathematical foundations of theoretical statistics. Philos Trans Royal Society London Ser A, 1922, 222: 309-368
[11] Forrester P J.Log-Gases and Random Matrices. Princeton: Princeton University Press, 2010
[12] Guillin A, Leonard C, Wu L, Yao N. Transportation-information inequalities for Markov processes. Probab Th Related Fields, 2009, 144: 669-695
[13] Gross L. Logarithmic Sobolev inequalities. Amer J Math, 1976, 97: 1061-1083
[14] Hastings S P, McLeod J B. A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation. Arch Rational Mech Anal, 1980, 73: 31-51
[15] Huang N, Ma Y.Limit theorems for β-Laguerre and β-Jacobi ensembles. Acta Math Sci, 2022, 42B: 2025-2039
[16] Jiang T. Limit theorems for beta-Jacobi ensembles. Bernoulli, 2013, 19(3): 1028-1046
[17] Jiang T, Li D. Approximation of rectangular beta-Laguerre ensembles and large deviations. J Theor Probab, 2015, 28: 804-847
[18] Jiang T, Ma Y. Distances between random orthogonal matrices and independent normals. Trans Amer Math Soc, 2019, 372: 1509-1553
[19] Johansson K. Shape fluctuation and random matrices. Commun Math Phys, 2000, 209: 437-476
[20] Johnstone I M. On the distribution of the largest eigenvalue in principal components analysis. Ann Stat, 2001, 29: 295-327
[21] Karoui N E.On the largest eigenvalue of Wishart matrices with identity covariance when n,p, and p/n→∞. arXiv:math/0309355
[22] Ledoux M, Rider B. Small deviations for Beta ensembles. Electron J Probab, 2010, 15: 1319-1343
[23] Ma Y, Shen X. Approximation of Beta-Jacobi ensembles by Beta-Laguerre ensembles. Front Math, 2023, 18: 225-252
[24] Muirhead R J.Aspects of Multivariate Statistical Theory. New York: Wiley, 1982
[25] Paul D.Asymptotic distribution of the smallest eigenvalue of Wishart (N,n) when N,n→∞ such that N/n→0//Jiang J, Roussas G G, Samaniego F J. Nonparametric Statistical Methods and Related Topics: A Festschrift in Honor of Professor P K Bhattacharya on the Occasion of His 80th Birthday. Singapore: World Scientific, 2011
[26] Ramírez J, Rider B, Virág B. Beta ensembles, stochastic Airy spectrum and a diffusion. J Amer Math Soc, 2011, 24(4): 919-944
[27] Soshnikov A. Universality at the edge of the spectrum in Wigner random matrices. Commun Math Phys, 1999, 207: 697-733
[28] Tao T, Vu V. Random matrices: University of local eigenvalue statistics up to the edge. Commun Math Phys, 2009, 298: 549-572
[29] Tracy C A, Widom H. Level-Spacing Distributions and the Airy Kernel. Commun Math Phys, 1994, 159: 151-174
[30] Tracy C A, Widom H. On orthogonal and symplectic matrix ensembles. Commun Math Phys, 1996, 177: 727-754 |