From random matrices to long range dependence

Chakrabarty, Arijit ; Hazra, Rajat Subhra ; Sarkar, Deepayan (2016) From random matrices to long range dependence Random Matrices: Theory and Applications, 05 (02). p. 1650008. ISSN 2010-3263

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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.

Item Type:Article
Source:Copyright of this article belongs to World Scientific Publishing Co Pte Ltd.
Keywords:Random Matrix; Long Range Dependence; Stationary Gaussian Process; Spectral Density.
ID Code:121023
Deposited On:08 Jul 2021 10:45
Last Modified:08 Jul 2021 10:45

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