ON LARGE DEVIATION REGIMES FOR RANDOM MEDIA MODELS

• 成果类型: Article
• 署名作者: Cranston, M.; Gauthier, D.; Mountford, T. S.
• 署名单位: University of California System; University of California Irvine; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP535
• 发表日期: 2009
• 页码: 826-862
• 关键词: 1st-passage percolation

摘要

The focus of this article is on the different behavior of large deviations of random subadditive functionals above the mean versus large deviations below the mean in two random media models. We consider the point-to-point first passage percolation time a(n) on Z(d) and a last passage percolation time Z(n). For these functionals, we have lim(n ->infinity) a(n)/n = v and lim(n ->infinity) Z(n)/n = mu. Typically, the large deviations for such functionals exhibits a strong asymmetry, large deviations above the limiting value are radically different from large deviations below this quantity. We develop robust techniques to quantify and explain the differences.