TITLE

Coupling, concentration inequalities, and stochastic dynamics

AUTHOR(S)
Chazottes, Jean-René; Collet, Pierre; Redig, Frank
PUB. DATE
December 2008
SOURCE
Journal of Mathematical Physics;Dec2008, Vol. 49 Issue 12, p125214
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In the context of interacting particle systems, we study the influence of the action of the semigroup on the concentration property of Lipschitz functions. As an application, this gives a new approach to estimate the relaxation speed to equilibrium of interacting particle systems. We illustrate our approach in a variety of examples for which we obtain several new results with short and nontechnical proofs. These examples include the symmetric and asymmetric exclusion processes and high-temperature spin-flip dynamics (“Glauber dynamics”). We also give a new proof of the Poincaré inequality, based on coupling, in the context of one-dimensional Gibbs measures. In particular, we cover the case of polynomially decaying potentials, where the log-Sobolev inequality does not hold.
ACCESSION #
35922189

 

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