In Compressive Sensing, the Restricted Isometry Property (RIP) ensures that robust recovery of sparsevectors is possible from noisy, undersampled measurements via computationally tractable algorithms. Itis by now well-known that Gaussian (or, more generally, sub-Gaussian) random matrices satisfy the RIPunder certain conditions on the number of measurements. Their use can be limi...

We propose an estimator for the mean of random variables in separable real Banach spaces using empirical characteristic function. Assuming that covariance operator variable is bounded a precise sense, we show proposed achieves optimal sub-Gaussian rate, except faster decaying mean-dependent term. Under mild condition, iterative refinement procedure can essentially eliminate term and provide shi...

Bounds for distributions of suprema $\varphi$-sub-Gaussian random fields defined over the $N$-dimensional unit sphere are stated. Applications results to spherical fractional Brownian motion, isotropic Gaussian and some other models presented.

This article provides a detailed analysis of the behavior of suprema and moduli of continuity for a large class of random fields which generalize Gaussian processes, sub-Gaussian processes, and random fields that are in the nth chaos of a Wiener process. An upper bound of Dudley type on the tail of the random field’s supremum is derived using a generic chaining argument; it implies similar resu...