Noncommutative Bennett and Rosenthal inequalities
Probability
2013-12-17 v4 Functional Analysis
Operator Algebras
Abstract
In this paper we extend the Bernstein, Prohorov and Bennett inequalities to the noncommutative setting. In addition we provide an improved version of the noncommutative Rosenthal inequality, essentially due to Nagaev, Pinelis and Pinelis, Utev for commutative random variables. We also present new best constants in Rosenthal's inequality. Applying these results to random Fourier projections, we recover and elaborate on fundamental results from compressed sensing, due to Candes, Romberg and Tao.
Keywords
Cite
@article{arxiv.1111.1027,
title = {Noncommutative Bennett and Rosenthal inequalities},
author = {Marius Junge and Qiang Zeng},
journal= {arXiv preprint arXiv:1111.1027},
year = {2013}
}
Comments
Published in at http://dx.doi.org/10.1214/12-AOP771 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)