Poincar\'{e} and transportation inequalities for Gibbs measures under the Dobrushin uniqueness condition

Liming Wu

doi:10.1214/009117906000000368

Poincar\'{e} and transportation inequalities for Gibbs measures under the Dobrushin uniqueness condition

Probability 2007-05-23 v1

Authors: Liming Wu

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Abstract

In in this paper we establish an explicit and sharp estimate of the spectral gap (Poincar\'{e} inequality) and the transportation inequality for Gibbs measures, under the Dobrushin uniqueness condition. Moreover, we give a generalization of the Liggett's $M-\epsilon$ theorem for interacting particle systems.

Keywords

gibbs measures poincaré inequality spectral gap transportation inequality dobrushin uniqueness condition interacting particle systems liggett theorem

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@article{arxiv.math/0611635,
  title  = {Poincar\'{e} and transportation inequalities for Gibbs measures under the Dobrushin uniqueness condition},
  author = {Liming Wu},
  journal= {arXiv preprint arXiv:math/0611635},
  year   = {2007}
}

Comments

Published at http://dx.doi.org/10.1214/009117906000000368 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Poincar\'{e} and transportation inequalities for Gibbs measures under the Dobrushin uniqueness condition

Abstract

Keywords

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