THE TIME CONSTANT FOR BERNOULLI PERCOLATION IS LIPSCHITZ CONTINUOUS STRICTLY ABOVE pc

• 成果类型: Article
• 署名作者: Cerf, Raphael; Dembin, Barbara
• 署名单位: Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/22-AOP1565
• 发表日期: 2022
• 页码: 1781-1812
• 关键词: chemical distance

摘要

We consider the standard model of i.i.d. first passage percolation on Z(d) given a distribution G on [0, +infinity] (-infinity is allowed). When G([0, +infinity)) > p(c) (d), it is known that the time constant mu(G) exists. We are interested in the regularity properties of the map G bar right arrow mu(G). We first study the specific case of distributions of the form G(p) = p delta(1) + (1 - p)delta(infinity) for p > p(c) (d). In this case, the travel time between two points is equal to the length of the shortest path between the two points in a bond percolation of parameter p. We show that the function p bar right arrow mu(Gp) is Lipschitz continuous on every interval [p(0), 1], where p(0) > p(c)(d).