On the Uniqueness of Global Multiple SLEs
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2018
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917744327262208 |
|---|---|
| author | Beffara, Vincent Peltola, Eveliina Wu, Hao |
| author_facet | Beffara, Vincent Peltola, Eveliina Wu, Hao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1801_07699 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On the Uniqueness of Global Multiple SLEs Beffara, Vincent Peltola, Eveliina Wu, Hao Probability Mathematical Physics 60J67, 82B20 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. |
| title | On the Uniqueness of Global Multiple SLEs |
| topic | Probability Mathematical Physics 60J67, 82B20 |
| url | https://arxiv.org/abs/1801.07699 |