ON THE NATURE OF THE SWISS CHEESE IN DIMENSION 3

• 成果类型: Article
• 署名作者: Asselah, Amine; Schapira, Bruno
• 署名单位: Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Aix-Marseille Universite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/19-AOP1380
• 发表日期: 2020
• 页码: 1002-1013
• 关键词: moderate deviations; random-walk; range; volume

摘要

We study scenarii linked with the Swiss cheese picture in dimension 3 obtained when two random walks are forced to meet often, or when one random walk is forced to squeeze its range. In the case of two random walks, we show that they most likely meet in a region of optimal density. In the case of one random walk, we show that a small range is reached by a strategy uniform in time. Both results rely on an original inequality estimating the cost of visiting sparse sites, and in the case of one random walk on the precise large deviation principle of van den Berg, Bolthausen and den Hollander (Ann. of Math. (2) 153 (2001) 355-406), including their sharp estimates of the rate functions in the neighborhood of the origin.