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

• 成果类型: Article
• 署名作者: Wu, Liming
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Clermont Auvergne (UCA); Wuhan University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000368
• 发表日期: 2006
• 页码: 1960-1989
• 关键词: logarithmic sobolev inequality; unbounded spin systems; random-variables; EQUIVALENCE; EXISTENCE; THEOREM

摘要

In in this paper we establish an explicit and sharp estimate of the spectral gap (Poincare 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.