From random matrices to long range dependence

Article Type

Research Article

Publication Title

Random Matrices: Theory and Application

Abstract

Random matrices whose entries come from a stationary Gaussian process are studied. The limiting behavior of the eigenvalues as the size of the matrix goes to infinity is the main subject of interest in this work. It is shown that the limiting spectral distribution is determined by the absolutely continuous component of the spectral measure of the stationary process. This is similar to the situation where the entries of the matrix are i.i.d. On the other hand, the discrete component contributes to the limiting behavior of the eigenvalues after a different scaling. Therefore, this helps to define a boundary between short and long range dependence of a stationary Gaussian process in the context of random matrices.

DOI

10.1142/S2010326316500088

Publication Date

4-1-2016

Comments

Open Access; Green Open Access

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