LARGE DEVIATIONS FOR INTERSECTION LOCAL TIMES IN CRITICAL DIMENSION

• 成果类型: Article
• 署名作者: Castell, Fabienne
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP499
• 发表日期: 2010
• 页码: 927-953
• 关键词: shear-flow drift; central limit-theorem; iterated logarithm; random-walks; Moderate Deviations; polymer-chains; INVARIANCE-PRINCIPLES; aleatory walks; random scenery; edwards model

摘要

Let (X(t), t >= 0) be a continuous time simple random walk on Z(d) (d >= 3), and let I(T)(x) be the time spent by (X(t), t >= 0) on the site x up to time T. We prove a large deviations principle for the q-fold self-intersection local time I(T) = Sigma(x is an element of Zd) I(T)(x)(q) in the critical case q = d/d-2. When q is integer, we obtain similar results for the intersection local times of q independent simple random walks.