Publications and Preprints
Limiting spectral distribution for Wigner matrices with dependent entries
by
Arijit Chakrabarty, Rajat Subhra Hazra and Deepayan Sarkar
In this article we show the existence of limiting spectral distribution of
a symmetric random matrix whose entries come from a stationary Gaussian
process with covariances satisfying a summability condition. We
provide an explicit description of the moments of the limiting
measure. We also show that in some special cases the Gaussian assumption
can be relaxed. The description of the limiting measure can also be
made via its Stieltjes transform which is characterized as the
solution of a functional equation. In two special cases, we get a
description of the limiting measure - one as a free product
convolution of two distributions, and the other one as a dilation of
the Wigner semicircular law.
isid/ms/2013/05 [fulltext]
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