Limiting spectral distribution of Gram matrices associated with functionals of β-mixing processes

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:433

Article

Banna, Marwa

关键词: Random matrices;    Sample covariance matrices;    Stieltjes transform;    Absolutely regular sequences;    Limiting spectral distribution;    Spectral density;   

DOI  :  10.1016/j.jmaa.2015.07.064

来源: Elsevier

【 摘 要 】

We give asymptotic spectral results for Gram matrices of the form n(-1)X(n)X(n)(T) where the entries of X-n are dependent across both rows and columns. More precisely, they consist of short or long range dependent random variables having moments of second order and that are functionals of an absolutely regular sequence. We also give a concentration inequality of the Stieltjes transform and we prove that, under an arithmetical decay condition on the beta-mixing coefficients, it is almost surely concentrated around its expectation. Applications to examples of positive recurrent Markov chains and dynamical systems are also given. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free