Concentration of the spectral measure of large Wishart matrices with dependent entries

We derive concentration inequalities for the spectral measure of large random matrices, allowing for certain forms of dependence. Our main focus is on empirical covariance (Wishart) matrices, but general symmetric random matrices are also considered.

[1]  Zhidong Bai,et al.  LARGE SAMPLE COVARIANCE MATRICES WITHOUT INDEPENDENCE STRUCTURES IN COLUMNS , 2008 .

[2]  Z. Bai,et al.  METHODOLOGIES IN SPECTRAL ANALYSIS OF LARGE DIMENSIONAL RANDOM MATRICES, A REVIEW , 2008 .

[3]  A. Mukherjea,et al.  Real and Functional Analysis , 1978 .

[4]  W. Hoeffding Probability Inequalities for sums of Bounded Random Variables , 1963 .

[5]  J. Walsh A Closed Set of Normal Orthogonal Functions , 1923 .

[6]  Colin McDiarmid,et al.  Surveys in Combinatorics, 1989: On the method of bounded differences , 1989 .

[7]  M. Talagrand A new look at independence , 1996 .

[8]  Z. Bai METHODOLOGIES IN SPECTRAL ANALYSIS OF LARGE DIMENSIONAL RANDOM MATRICES , A REVIEW , 1999 .

[9]  A. Guionnet Large deviations and stochastic calculus for large random matrices , 2004, math/0409277.

[10]  S. Mendelson,et al.  On singular values of matrices with independent rows , 2006 .

[11]  CONVEX MULTIVARIABLE TRACE FUNCTIONS , 2001, math/0107062.

[12]  B. Maurey Some deviation inequalities , 1990, math/9201216.

[13]  S. Lang Real and Functional Analysis , 1983 .

[14]  H. Chernoff A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations , 1952 .

[15]  F. Gotze,et al.  Limit Theorems for Spectra of Positive Random Matrices under Dependence , 2006 .

[16]  A. Guionnet,et al.  CONCENTRATION OF THE SPECTRAL MEASURE FOR LARGE MATRICES , 2000 .

[17]  Kazuoki Azuma WEIGHTED SUMS OF CERTAIN DEPENDENT RANDOM VARIABLES , 1967 .

[18]  P. MassartLedoux,et al.  Concentration Inequalities Using the Entropy Method , 2002 .

[19]  C. Houdr'e,et al.  Concentration of the Spectral Measure for Large Random Matrices with Stable Entries , 2007, 0706.1753.