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- W1787366875 abstract "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'e 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." @default.
- W1787366875 created "2016-06-24" @default.
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- W1787366875 date "2012-11-14" @default.
- W1787366875 modified "2023-10-16" @default.
- W1787366875 title "Noncommutative martingale deviation and Poincar'e type inequalities with applications" @default.
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- W1787366875 doi "https://doi.org/10.48550/arxiv.1211.3209" @default.
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