MODERATE DEVIATIONS OF DEPENDENT RANDOM-VARIABLES RELATED TO CLT

• 成果类型: Article
• 署名作者: WU, LM
• 署名单位: Wuhan University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1995
• 页码: 420-445
• 关键词: irreducible markov-processes; random-fields; temperature; sums

摘要

This paper consists of three parts. In the first part, we find a common condition-the C-2-regularity-both for CLT and for moderate deviations. We show that this condition is verified in two important situations: the Lee-Yang theorem case and the FKG system case. In the second part; we apply the previous results to the additive functionals of a Markov process. By means of Feymman-Kac formula and Kato's analytic perturbation theory, we show that the Lee-Yang theorem holds under the assumption that 1 is an isolated, simple and the only eigenvalue with modulus 1 of the operator P-1 acting on an appropriate Banach space (bE,C-b(E), L(2)...). The last part is devoted to some applications to statistical mechanical systems, where the C-2-regularity becomes a property of the pressure functionals and the two situations presented above become exactly the Lee-Yang theorem case and the FKG system case. We shall discuss in detail the ferromagnetic model and give some general remarks on some other models.