Theoretical Statistics and Mathematics Unit, ISI Delhi

From random matrices to long range dependence

by Arijit Chakrabarty, Rajat Subhra Hazra and Deepayan Sarkar

Random matrices whose entries come from a stationary Gaussian process are
studied. The limiting behaviour 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, a phenomenon resembling that in 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 in a completely different way. Therefore, this helps to
define a boundary between short and long range dependence of a stationary
Gaussian process in the context of random matrices.

isid/ms/2014/01 [fulltext]

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