Extreme eigenvalues of m-dependent heavy-tailed matrices

Abstract

We analyze the largest eigenvalue statistics of two standard types of symmetric random matrix models having entry-wise regularly varying tail distributions with parameter 0 < $\alpha$ < 4. Our analysis extends results in the previous literature for symmetric matrices with independent entries above the diagonal, by allowing for m-dependence between the entries of a given matrix. We prove that the limiting point process of extreme eigenvalues is a Poisson cluster process.