Poincaré and transportation inequalities for Gibbs measures under the Dobrushin uniqueness condition

2006/09/01 by Liming Wu · 2 citations
Mathematics · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Stochastic processes and statistical mechanics #math.PR #msc:60E15 #msc:60G60 #msc:60K35

paper · pdf · doi:10.1214/009117906000000368

published as Annals of Probability 2006, Vol. 34, No. 5, 1960-1989 · 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)

openalex publication_date 2006/09/01 · arxiv created 2006/11/21 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In in this paper we establish an explicit and sharp estimate of the spectral gap (Poincaré inequality) and the transportation inequality for Gibbs measures, under the Dobrushin uniqueness condition. Moreover, we give a generalization of the Liggett’s M−ɛ theorem for interacting particle systems.

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