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arXiv · 0708.2152

Coupling, concentration inequalities and stochastic dynamics

Jean René Chazottes·Pierre Collet·Frank Redig
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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 non-technical proofs. These examples include the symmetric and asymmetric exclusion process 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.

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Jean René Chazottes, Pierre Collet, Frank Redig. 2015-06-29. Coupling, concentration inequalities and stochastic dynamics. https://arxiv.org/abs/0708.2152

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