On log-concave-tailed chaoses and the restricted isometry property

Abstract

In this paper, we obtain a p-th moment bound for the suprema of a log-concave-tailed nonhomogeneous chaos process, which is optimal in some cases. With this p-th moment bound, we get two uniform Hanson-Wright type deviation inequalities for α-subexponential entries ($1\le \alpha \le 2$), which generalize some known results. As applications, we prove the restricted isometry property of partial random circulant matrices and time-frequency structured random matrices induced by α-subexponential vectors ($1\le \alpha \le 2$), which extends the previously known results proved in the subgaussian case.