Critical percolation exploration path and SLE 6:: a proof of convergence

• 成果类型: Article
• 署名作者: Camia, Federico; Newman, Charles M.
• 署名单位: Vrije Universiteit Amsterdam; New York University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-006-0049-7
• 发表日期: 2007
• 页码: 473-519
• 关键词: uniform spanning-trees; erased random-walks; conformal-invariance; critical exponents; cardys formula; plane

摘要

It was argued by Schramm and Smirnov that the critical site percolation exploration path on the triangular lattice converges in distribution to the trace of chordal SLE6. We provide here a detailed proof, which relies on Smirnov's theorem that crossing probabilities have a conformally invariant scaling limit (given by Cardy's formula). The version of convergence to SLE (6) that we prove suffices for the Smirnov-Werner derivation of certain critical percolation crossing exponents and for our analysis of the critical percolation full scaling limit as a process of continuum nonsimple loops.