On the limiting spectral distribution for a large class of symmetric random matrices with correlated entries

Marwa Banna, Florence Merlevède and Magda Peligrad

Stochastic Processes and their Applications, 2015, vol. 125, issue 7, 2700-2726

Abstract: For symmetric random matrices with correlated entries, which are functions of independent random variables, we show that the asymptotic behavior of the empirical eigenvalue distribution can be obtained by analyzing a Gaussian matrix with the same covariance structure. This class contains both cases of short and long range dependent random fields. The technique is based on a blend of blocking procedure and Lindeberg’s method. This method leads to a variety of interesting asymptotic results for matrices with dependent entries, including applications to linear processes as well as nonlinear Volterra-type processes entries.

Keywords: Random matrices; Correlated entries; Sample covariance matrices; Weak dependence; Limiting spectral distribution (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (6)

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DOI: 10.1016/j.spa.2015.01.010

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