Uniform Hanson-Wright Type Deviation Inequalities for α-Subexponential Random Vectors
Abstract
The work establishes uniform Hanson-Wright inequalities for α-subexponential random vectors via decoupling and moment comparisons, then applies them to prove restricted isometry properties of partial random circulant matrices.
This paper is devoted to uniform versions of the Hanson-Wright inequality for a random vector with independent centered α-subexponential entries, 0<αle 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<αle 1.
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