NONCOMMUTATIVE BENNETT AND ROSENTHAL INEQUALITIES

• 成果类型: Article
• 署名作者: Junge, Marius; Zeng, Qiang
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP771
• 发表日期: 2013
• 页码: 4287-4316
• 关键词: constants; reconstruction; khintchine; SPACES

摘要

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.