On Log-Concave-Tailed Chaos and the Restricted Isometry Property

We develop a novel decoupling inequality for nonhomogeneous order 2 non-Gaussian chaoses. Having this decoupling inequality, we show two types of the p-th moment bounds for the suprema of a log-concave-tailed chaos process based on some chaining techniques and the generalized majorizing measure theorems for canonical processes. As applications, we show the restricted isometry property of partial random circulant matrices and time-frequency structured random matrices induced by standard α-subexponential vectors, 1≤α≤ 2, which extends the previously known results for the sub-Gaussian case.