Noncommutative bennett and rosenthal inequalities

Marius Junge*, Qiang Zeng

*Corresponding author for this work

Research output: Contribution to journalArticle

19 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)4287-4316
Number of pages30
JournalAnnals of Probability
Volume41
Issue number6
DOIs
StatePublished - Nov 1 2013

Keywords

  • (Noncommutative) Bennett inequality
  • (Noncommutative) Bernstein inequality
  • (Noncommutative) Prohorov inequality
  • (Noncommutative) Rosenthal inequality
  • Compressed sensing
  • Cramér's theorem
  • Large deviation
  • Noncommutative Lp spaces

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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