Theoretical Statistics and Mathematics Unit, ISI Delhi

Maximum eigenvalue of symmetric random matrices with dependent heavy tailed entries

by Arijit Chakrabarty, Rajat Subhra Hazra and Parthanil Roy

This paper deals with symmetric random matrices whose upper diagonal entries are obtained from a linear random field with heavy tailed noise. It is shown that the maximum eigenvalue and the spectral radius of such a random matrix with dependent entries converge to the Frech\'et distribution after appropriate scaling. This extends a seminal result of Soshnikov [A.~Soshnikov, Poisson statistics for the largest eigenvalues of {W}igner random matrices with heavy tails. \emph{Electron. Comm. Probab.}, 9:\penalty0 82--91 (electronic), 2004] when the tail index is strictly less than one.

isid/ms/2013/09 [fulltext]

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