2012/08/19 by Alan Hammond, Hammond, Alan, Gábor Pete +3 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1208.3826
openalex publication_date 2012/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In dynamical critical site percolation on the triangular lattice or bond\npercolation on Z2, we define and study a local time measure on the\nexceptional times at which the origin is in an infinite cluster. We show that\nat a typical time with respect to this measure, the percolation configuration\nhas the law of Kesten's Incipient Infinite Cluster. In the most technical\nresult of this paper, we show that, on the other hand, at the first exceptional\ntime, the law of the configuration is different. We also study the collapse of\nthe infinite cluster near typical exceptional times, and establish a relation\nbetween static and dynamic exponents, analogous to Kesten's near-critical\nrelation.\n