On the uniqueness of global multiple SLEs

Vincent Beffara Institut Fourier, CNRS & University Grenoble Alpes Eveliina Peltola Institute for Applied Mathematics, University of Bonn Hao Wu Yau Mathematical Sciences Center, Tsinghua University

Probability mathscidoc:2105.28001

The annals of probability, 49, (1), 400-434, 2021.3
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.
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@inproceedings{vincent2021on,
  title={On the uniqueness of global multiple SLEs},
  author={Vincent Beffara, Eveliina Peltola, and Hao Wu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210511110257297956819},
  booktitle={The annals of probability},
  volume={49},
  number={1},
  pages={400-434},
  year={2021},
}
Vincent Beffara, Eveliina Peltola, and Hao Wu. On the uniqueness of global multiple SLEs. 2021. Vol. 49. In The annals of probability. pp.400-434. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210511110257297956819.
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