On the spectral norm of large heavy-tailed random matrices with strongly dependent rows and columns

Abstract

We study a new random matrix ensemble $X$ which is constructed by an application of a two dimensional linear filter to a matrix of iid random variables with infinite fourth moments. Our result gives asymptotic lower and upper bounds for the spectral norm of the (centered) sample covariance matrix $XX^\T$ when the number of columns as well es the number of rows of $X$ tend to infinity.