Noncommutative Bennett and Rosenthal inequalities

Marius Junge ^[1] ; Qiang Zeng ^[1]
1. [1] University of Illinois at Urbana Champaign
  
  University of Illinois at Urbana Champaign
  
  Township of Cunningham, Estados Unidos
Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 6, 2013, págs. 4287-4316
Idioma: inglés
DOI: 10.1214/12-AOP771
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Resumen
- 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.