Maximum eigenvalue of symmetric random matrices with dependent heavy tailed entries
Probability
2014-06-12 v2
Abstract
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(2004) when the tail index is strictly less than one.
Cite
@article{arxiv.1309.1407,
title = {Maximum eigenvalue of symmetric random matrices with dependent heavy tailed entries},
author = {Arijit Chakrabarty and Rajat Subhra Hazra and Parthanil Roy},
journal= {arXiv preprint arXiv:1309.1407},
year = {2014}
}
Comments
This article is withdrawn due to a gap in Step 4 of the proof of Theorem 1.1