On the expectation of operator norms of random matrices

TL;DR

This paper provides estimates for the expected operator norms of Gaussian random matrices acting between specific  spaces, advancing understanding of their probabilistic behavior in high-dimensional settings.

Contribution

It introduces new bounds for the expected operator norms of Gaussian matrices between  spaces with different p and q norms, extending previous results.

Findings

Derived bounds for Gaussian matrix operator norms between  spaces

Applicable to matrices with independent, mean-zero entries

Enhances understanding of high-dimensional random matrix behavior

Abstract

We prove estimates for the expected value of operator norms of Gaussian random matrices with independent and mean-zero entries, acting as operators from $\ell^m_{p^*}$ to $\ell_q^n$, $1\leq p^* \leq 2 \leq q \leq \infty$.