Uniform Hanson-Wright Type Deviation Inequalities for $\hat{I}\pm$-Subexponential Random Vectors

Abstract

This paper is devoted to uniform versions of the Hanson-Wright inequality for a random vector with independent centered $\hat{I}\pm$-subexponential entries, $0<\hat{I}\pm \le 1$. 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 $\hat{I}\pm$-subexponential random vectors, $0<\hat{I}\pm \le 1$.

arXiv admin note: text overlap with arXiv:2401.14860