LARGE DEVIATIONS AND MAXIMUM-ENTROPY PRINCIPLE FOR INTERACTING RANDOM-FIELDS ON Z(D)

• 成果类型: Article
• 署名作者: GEORGII, HO
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989002
• 发表日期: 1993
• 页码: 1845-1875
• 关键词: markov process expectations; asymptotic evaluation; LIMIT-THEOREMS; large time; vector

摘要

We present a new approach to the principle of large deviations for the empirical field of a Gibbsian random field on the integer lattice Z(d). This approach has two main features. First, we can replace the traditional weak topology by the finer topology of convergence of cylinder probabilities, and thus obtain estimates which are finer and more widely applicable. Second, we obtain as an immediate consequence a limit theorem for conditional distributions under conditions on the empirical field, the limits being those predicted by the maximum entropy principle. This result implies a general version of the equivalence of Gibbs ensembles, stating that every microcanonical limiting state is a grand canonical equilibrium state. We also prove a converse to the last statement, and discuss some applications.