Quenched invariance principle for simple random walk on clusters in correlated percolation models

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• 作者：Eviatar B. Procaccia ; Ron Rosenthal…
• 关键词：Mathematics Subject Classification60F17 ; 60G50 ; 60K35 ; 82B41 ; 82B43
• 刊名：Probability Theory and Related Fields
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：166
• 期：3-4
• 页码：619-657
• 全文大小：1,792 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Probability Theory and Stochastic Processes
  Mathematical and Computational Physics
  Quantitative Finance
  Mathematical Biology
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Operation Research and Decision Theory
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-2064
• 卷排序：166

文摘

We prove a quenched invariance principle for simple random walk on the unique infinite percolation cluster for a general class of percolation models on \({\mathbb {Z}}^d\), \(d\ge 2\), with long-range correlations introduced in (Drewitz et al. in J Math Phys 55(8):083307, 2014), solving one of the open problems from there. This gives new results for random interlacements in dimension \(d\ge 3\) at every level, as well as for the vacant set of random interlacements and the level sets of the Gaussian free field in the regime of the so-called local uniqueness (which is believed to coincide with the whole supercritical regime). An essential ingredient of our proof is a new isoperimetric inequality for correlated percolation models.