On the expectation of the norm of random matrices with non-identically distributed entries

Abstract

Let $X_{i,j}$, $i,j=1,...,n$, be independent, not necessarily identically distributed random variables with finite first moments. We show that the norm of the random matrix $(X_{i,j})_{i,j=1}^n$ is up to a logarithmic factor of the order of $\mathbb{E}\max\limits_{i=1,...,n}\left\Vert(X_{i,j})_{j=1}^n\right\Vert_2+\mathbb{E}\max\limits_{i=1,...,n}\left\Vert(X_{i,j})_{j=1}^n\right\Vert_2$. This extends (and improves in most cases) the previous results of Seginer and Latala.