ON THE UNIQUENESS OF GLOBAL MULTIPLE SLES

• 成果类型: Article
• 署名作者: Beffara, Vincent; Peltola, Eveliina; Wu, Hao
• 署名单位: Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); University of Bonn; Tsinghua University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1477
• 发表日期: 2021
• 页码: 400-434
• 关键词: erased random-walks; conformal-invariance; critical percolation; ising interfaces; SCALING LIMITS; random-cluster; RESTRICTION; path

摘要

This article focuses on the characterization of global multiple Schramm-Loewner evolutions (SLE). The chordal SLE describes the scaling limit of a single interface in various critical lattice models with Dobrushin boundary conditions, and similarly, global multiple SLEs describe scaling limits of collections of interfaces in critical lattice models with alternating boundary conditions. In this article, we give a minimal amount of characterizing properties for the global multiple SLEs: we prove that there exists a unique probability measure on collections of pairwise disjoint continuous simple curves with a certain conditional law property. As a consequence, we obtain the convergence of multiple interfaces in the critical Ising, FK-Ising and percolation models.