Open Access
November 2013 Noncommutative Bennett and Rosenthal inequalities
Marius Junge, Qiang Zeng
Ann. Probab. 41(6): 4287-4316 (November 2013). DOI: 10.1214/12-AOP771


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.


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Marius Junge. Qiang Zeng. "Noncommutative Bennett and Rosenthal inequalities." Ann. Probab. 41 (6) 4287 - 4316, November 2013.


Published: November 2013
First available in Project Euclid: 20 November 2013

zbMATH: 1290.46056
MathSciNet: MR3161475
Digital Object Identifier: 10.1214/12-AOP771

Primary: 46L53 , 60E15
Secondary: 46L52 , 60F10 , 94A12

Keywords: (Noncommutative) Bennett inequality , (noncommutative) Bernstein inequality , (noncommutative) Prohorov inequality , (noncommutative) Rosenthal inequality , compressed sensing , Cramér’s theorem , large deviation , noncommutative $L_{p}$ spaces

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 6 • November 2013
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