Uniform Hanson-Wright Type Deviation Inequalities for α-Subexponential Random Vectors

This paper is devoted to uniform versions of the Hanson-Wright inequality for a random vector with independent centered α-subexponential entries, 0<α≤ 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 α-subexponential random vectors, 0<α≤ 1.