Uniform Hanson-Wright Type Deviation Inequalities for $\alpha$-Subexponential Random Vectors

TL;DR

This paper establishes uniform Hanson-Wright deviation inequalities for $ ext{alpha}$-subexponential vectors, providing tools for analyzing random matrices and their properties.

Contribution

It introduces a novel decoupling inequality and compares weak and strong moments to extend Hanson-Wright inequalities to $ ext{alpha}$-subexponential vectors.

Findings

Proves uniform Hanson-Wright inequalities for $ ext{alpha}$-subexponential vectors

Demonstrates the restricted isometry property for partial random circulant matrices

Develops a new decoupling inequality for $ ext{alpha}$-subexponential variables

Abstract

This paper is devoted to uniform versions of the Hanson-Wright inequality for a random vector with independent centered $\alpha$-subexponential entries, $0<\alpha\le 1$. Our method relies upon a novel decoupling inequality and a comparison of weak and strong moments. As an application, we use the derived inequality to prove the restricted isometry property of partial random circulant matrices generated by standard $\alpha$-subexponential random vectors, $0<\alpha\le 1$.