Critical exponents of planar gradient percolation

• 成果类型: Article
• 署名作者: Nolin, Pierre
• 署名单位: Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Saclay
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/07-AOP375
• 发表日期: 2008
• 页码: 1748-1776
• 关键词: brownian intersection exponents; SCALING LIMITS; 2d percolation; probability; VALUES

摘要

We study gradient percolation for site percolation on the triangular lattice. This is a percolation model where the percolation probability depends linearly on the location of the site. We prove the results predicted by physicists for this model. More precisely, we describe the fluctuations of the interfaces around their (straight) scaling limits, and the expected and typical lengths of these interfaces. These results build on the recent results for critical percolation on this lattice by Smirnov, Lawler, Schramm and Werner, and on the scaling ideas developed by Kesten .