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January 2021 On the uniqueness of global multiple SLEs
Vincent Beffara, Eveliina Peltola, Hao Wu
Ann. Probab. 49(1): 400-434 (January 2021). DOI: 10.1214/20-AOP1477

Abstract

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.

Citation

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Vincent Beffara. Eveliina Peltola. Hao Wu. "On the uniqueness of global multiple SLEs." Ann. Probab. 49 (1) 400 - 434, January 2021. https://doi.org/10.1214/20-AOP1477

Information

Received: 1 April 2018; Revised: 1 June 2020; Published: January 2021
First available in Project Euclid: 22 January 2021

Digital Object Identifier: 10.1214/20-AOP1477

Subjects:
Primary: 60J67, 60K35

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 1 • January 2021
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