Noncommutative martingale deviation and Poincaré type inequalities with applications

By Marius Junge, Qiang Zeng. 2012

57 citations recorded by the source corpus.

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 Poincaré 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 Götze 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.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/125a775e97c5ece507bd12d07e433d2c0429b9cf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Jan Maas
2. Eric A. Carlen
3. Marco Cuturi
4. G. Peyr'e

In Statistics and Probability

1. Jan Maas
2. Eric A. Carlen

Citations in the corpus

• Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance (2016, background): “Also, Junge and Zeng [38] have recently developed an approach to some non-commutative functional inequalities involving a non-commutative analog of the 1-Wasserstein metric.”