Slow decay of Gibbs measures with heavy tails

• 成果类型: Article
• 署名作者: Roberto, Cyril
• 署名单位: Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-009-0229-3
• 发表日期: 2010
• 页码: 247-268
• 关键词: logarithmic sobolev inequalities; particle-systems; spectral gap; PROBABILITY-MEASURES; poincare; CONVERGENCE; equilibrium; DYNAMICS; entropy; rates

摘要

We consider Glauber dynamics reversible with respect to Gibbs measures with heavy tails in the case when spins are unbounded. The interactions are bounded and of finite range. The self-potential enters into two classes of measures, kappa-concave probability measures and sub-exponential laws, for which it is known that no exponential decay can occur. Using coercive inequalities we prove that, for kappa-concave probability measures, the associated infinite volume semi-group decays to equilibrium polynomially and stretched exponentially for sub-exponential laws. This improves and extends previous results by Bobkov and Zegarlinski.