Large deviations in first-passage percolation

• 成果类型: Article
• 署名作者: Chow, Y; Zhang, Y
• 署名单位: Academia Sinica - Taiwan; University of Colorado System; University of Colorado at Colorado Springs
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2003
• 页码: 1601-1614
• 关键词: passage percolation

摘要

Consider the standard first-passage percolation on Z(d), d greater than or equal to 2. Denote by phi(0,n) the face-face first-passage time in [0, n](d). It is well known that Lim(n-->infinity) phi0,n/n = mu(F) a.s. and in L-1, where F is the common distribution on each edge. In this paper we show that the upper and lower tails of phi(0,n) are quite different when mu(F) > 0. More precisely, we can show that for small epsilon > 0, there exist constants alpha(epsilon, F) and beta(epsilon, F) such that lim(n-->infinity) -1/n log P (phi(0, n1.)less than or equal to n (mu - epsilon)) = alpha (epsilon, F) and lim(n-->infinity) -1/n(d) log P (phi(0,n) greater than or equal to n(mu + epsilon)) = alpha(epsilon, F).