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Noncommutative Bennett and Rosenthal inequalities

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arxiv 1111.1027 v4 pith:LLYWM7YB submitted 2011-11-04 math.PR math.FAmath.OA

Noncommutative Bennett and Rosenthal inequalities

Marius Junge , Qiang Zeng This is my paper
classification math.PR math.FAmath.OA
keywords noncommutativerosenthalbennettinequalitiesinequalitypinelisrandomresults
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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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