A HSU-ROBBINS-ERDOS STRONG LAW IN FIRST-PASSAGE PERCOLATION

• 成果类型: Article
• 署名作者: Ahlberg, Daniel
• 署名单位: Instituto Nacional de Matematica Pura e Aplicada (IMPA)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP926
• 发表日期: 2015
• 页码: 1992-2025
• 关键词: supercritical bernoulli percolation; 1st passage percolation; chemical distance; large deviations

摘要

Large deviations in the context of first-passage percolation was first studied in the early 1980s by Grimmett and Kesten, and has since been revisited in a variety of studies. However, none of these studies provides a precise relation between the existence of moments of polynomial order and the decay of probability tails. Such a relation is derived in this paper, and is used to strengthen the conclusion of the shape theorem. In contrast to its one-dimensional counterpart-the Hsu-Robbins-Erdos strong law-this strengthening is obtained without imposing a higher-order moment condition.