Chevet-type inequalities for subexponential Weibull variables and estimates for norms of random matrices

TL;DR

This paper establishes Chevet-type inequalities for subexponential Weibull variables and uses them to derive bounds on the norms of certain random matrices, advancing understanding of their behavior in high-dimensional probability.

Contribution

It introduces new Chevet-type inequalities for Weibull variables and applies these to estimate norms of random matrices with Weibull and log-concave entries.

Findings

Two-sided bounds for operator norms of Weibull-based random matrices

Estimates for maximal submatrix norms in Weibull and log-concave cases

Extension of Chevet inequalities to subexponential Weibull variables

Abstract

We prove two-sided Chevet-type inequalities for independent symmetric Weibull random variables with shape parameter $r\in[1,2]$. We apply them to provide two-sided estimates for operator norms from $\ell_p^n$ to $\ell_q^m$ of random matrices $(a_ib_jX_{i,j})_{i\le m, j\le n}$, in the case when $X_{i,j}$'s are iid symmetric Weibull variables with shape parameter $r\in[1,2]$ or when $X$ is an isotropic log-concave unconditional random matrix. We also show how these Chevet-type inequalities imply two-sided bounds for maximal norms from $\ell_p^n$ to $\ell_q^m$ of submatrices of $X$ in both Weibull and log-concave settings.