Noncommutative martingale deviation and Poincar, type inequalities with applications

• 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: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-014-0552-1
• 发表日期: 2015
• 页码: 449-507
• 关键词: riesz transforms; continuity

摘要

We prove a deviation inequality for noncommutative martingales by extending Oliveira's argument for random matrices. By integration we obtain a Burkholder type inequality with satisfactory constant. Using continuous time, we establish noncommutative Poincar, type inequalities for nice semigroups with a positive curvature condition. These results allow us to prove a general deviation inequality and a noncommutative transportation inequality due to Bobkov and Gotze in the commutative case. To demonstrate our setting is general enough, we give various examples, including certain group von Neumann algebras, random matrices and classical diffusion processes, among others.