LOCAL TIME ON THE EXCEPTIONAL SET OF DYNAMICAL PERCOLATION AND THE INCIPIENT INFINITE CLUSTER

• 成果类型: Article
• 署名作者: Hammond, Alan; Pete, Gabor; Schramm, Oded
• 署名单位: University of Oxford; Budapest University of Technology & Economics
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP950
• 发表日期: 2015
• 页码: 2949-3005
• 关键词: high-dimensional percolation; invasion percolation; noise sensitivity; SCALING LIMITS

摘要

In dynamical critical site percolation on the triangular lattice or bond percolation on Z(2), we define and study a local time measure on the exceptional times at which the origin is in an infinite cluster. We show that at a typical time with respect to this measure, the percolation configuration has the law of Kesten's incipient infinite cluster. In the most technical result of this paper, we show that, on the other hand, at the first exceptional time, the law of the configuration is different. We believe that the two laws are mutually singular, but do not show this. We also study the collapse of the infinite cluster near typical exceptional times and establish a relation between static and dynamic exponents, analogous to Kesten's near-critical relation.