GEOGRAPHY OF LOCAL CONFIGURATIONS

• 成果类型: Article
• 署名作者: Coupier, David
• 署名单位: Universite de Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP630
• 发表日期: 2010
• 页码: 806-840
• 关键词: poisson approximations; patterns

摘要

A d-dimensional binary Markov random field on a lattice torus is considered. As the size n of the lattice tends to infinity, potentials a = a (n) and b = b(n) depend on n. Precise bounds for the probability for local configurations to occur in a large ball are given. Under some conditions bearing on a (n) and b(n), the distance between copies of different local configurations is estimated according to their weights. Finally, a sufficient condition ensuring that a given local configuration occurs everywhere in the lattice is suggested.