This is an announcement for the paper "Noncommutative Bennett and Rosenthal Inequalities" by Marius Junge and Qiang Zeng.

Abstract: In this paper we extend Bennett's and Bernstein's inequality 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.

Archive classification: math.PR math.FA math.OA

Mathematics Subject Classification: 46L53, 46L50, 60E15, 60F10, 94A12

Remarks: 28 pages

Submitted from: zeng8@illinois.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1111.1027

or

http://arXiv.org/abs/1111.1027