ON THE SCALING LIMITS OF PLANAR PERCOLATION

• 成果类型: Article
• 署名作者: Schramm, Oded; Smirnov, Stanislav; Garban, Christophe
• 署名单位: University of Geneva; Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP659
• 发表日期: 2011
• 页码: 1768-1814
• 关键词: conformal-invariance; bond percolation; trees

摘要

We prove Tsirelson's conjecture that any scaling limit of the critical planar percolation is a black noise. Our theorems apply to a number of percolation models, including site percolation on the triangular grid and any subsequential scaling limit of bond percolation on the square grid. We also suggest a natural construction for the scaling limit of planar percolation, and more generally of any discrete planar model describing connectivity properties.