Maximum eigenvalue of symmetric random matrices with dependent heavy tailed entries

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 Frechét distribution after appropriate scaling. This extends a seminal result of Soshnikov(2004) when the tail index is strictly less than one.

This article is withdrawn due to a gap in Step 4 of the proof of Theorem 1.1

References in corpus (1)

• Limiting spectral distribution of a new random matrix model with dependence across rows and columns