A Universality Result for the Smallest Eigenvalues of Certain Sample Covariance Matrices

被引：0
|
作者：
Ohad N. Feldheim
Sasha Sodin
机构：
[1] Tel Aviv University,School of Mathematical Sciences, Sackler Faculty of Exact Sciences
来源：
Geometric and Functional Analysis | 2010年 / 20卷
关键词：
Universality; sample covariance; Tracy Widom; non-backtracking paths; 60B260B200;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
After proper rescaling and under some technical assumptions, the smallest eigenvalue of a sample covariance matrix with aspect ratio bounded away from 1 converges to the Tracy–Widom distribution. This complements the results on the largest eigenvalue, due to Soshnikov and Péché.
引用
收藏
页码：88 / 123
页数：35
相关论文
共 50 条
  • [41] On eigenvalues of certain special matrices
    Devi, Manisha
    Aujla, Jaspal Singh
    LINEAR & MULTILINEAR ALGEBRA, 2024,
  • [42] EIGENVALUES OF CERTAIN OPERATORS ON MATRICES
    HAUSNER, M
    COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1961, 14 (02) : 155 - &
  • [43] EIGENVALUES OF CERTAIN SPARSE MATRICES
    Al-Ashhab, Saloom
    MATEMATICKI VESNIK, 2013, 65 (02): : 234 - 241
  • [44] Large sample approximations for the LR statistic for equality of the smallest eigenvalues of a covariance matrix under elliptical population
    Watanabe, Daisuke
    Okada, Susumu
    Fujikoshi, Yasunori
    Sugiyama, Takakazu
    COMPUTATIONAL STATISTICS & DATA ANALYSIS, 2008, 52 (05) : 2714 - 2724
  • [45] LIMITING LAWS FOR DIVERGENT SPIKED EIGENVALUES AND LARGEST NONSPIKED EIGENVALUE OF SAMPLE COVARIANCE MATRICES
    Cai, T. Tony
    Han, Xiao
    Pan, Guangming
    ANNALS OF STATISTICS, 2020, 48 (03): : 1255 - 1280
  • [46] Almost sure convergence of the largest and smallest eigenvalues of high-dimensional sample correlation matrices
    Heiny, Johannes
    Mikosch, Thomas
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2018, 128 (08) : 2779 - 2815
  • [47] ASYMPTOTIC INDEPENDENCE OF SPIKED EIGENVALUES AND LINEAR SPECTRAL STATISTICS FOR LARGE SAMPLE COVARIANCE MATRICES
    Zhang, Zhixiang
    Zheng, Shurong
    Pan, Guangming
    Zhong, Ping-Shou
    ANNALS OF STATISTICS, 2022, 50 (04): : 2205 - 2230
  • [48] Universality in the fluctuation of eigenvalues of random circulant matrices
    Adhikari, Kartick
    Saha, Koushik
    STATISTICS & PROBABILITY LETTERS, 2018, 138 : 1 - 8
  • [49] On the Bias in Eigenvalues of Sample Covariance Matrix
    Hayashi, Kentaro
    Yuan, Ke-Hai
    Liang, Lu
    QUANTITATIVE PSYCHOLOGY, 2018, 233 : 221 - 233
  • [50] ON BOUNDS FOR THE SMALLEST AND THE LARGEST EIGENVALUES OF GCD AND LCM MATRICES
    Altinisik, Ercan
    Buyukkose, Serife
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2016, 19 (01): : 117 - 125
12345