SLE intersecting with random hulls

Yong Han; Yuefei Wang; Michel Zinsmeister

doi:10.1016/j.crma.2019.04.005

Probability theory

SLE intersecting with random hulls

Presented by: the Editorial Board

Yong Han ¹; Yuefei Wang ²; Michel Zinsmeister ³

¹ Yau Mathematical Sciences Center, Tsinghua University, Beijng, 100084, China
² Institute of Mathematics, Academy of Mathematics and Systems Sciences and University of the Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100190, China
³ IDP, Université d'Orléans, BP 6759, 45067 Orléans cedex 2, France

Comptes Rendus. Mathématique, Volume 357 (2019) no. 4, pp. 395-400.

Abstract
Résumé

Lawler, Schramm, and Werner gave in 2003 an explicit formula of the probability that $SLE (8 / 3)$ does not intersect a deterministic hull. For general $SLE (κ)$ with $κ \neq 8 / 3$ , no such explicit formula has been obtained so far. In this paper, we shall consider a random hull generated by an independent chordal conformal restriction measure and obtain an explicit formula for the probability that $SLE (κ)$ does not intersect this random hull for any $κ \in (0, 8)$ . As a corollary, we will give a new proof of Werner's result on conformal restriction measures.

Lawler, Schramm et Werner ont donné en 2003 une formule explicite pour la probabilité que $SLE (8 / 3)$ ne rencontre pas une enveloppe déterministe. Pour $SLE (κ)$ avec $κ \neq 8 / 3$ , aucune formule de ce type ne semble connue. Nous considérons ici une enveloppe aléatoire engendrée par une mesure de restriction conforme indépendante et nous obtenons une formule explicite de la probabilité que $SLE (κ)$ ne la rencontre pas lorsque $κ \in (0, 8)$ . Comme corollaire, nous donnons une nouvelle démonstration d'un résultat de Werner sur les mesures de restrictions conformes.

Received: 2018-08-11
Accepted: 2019-04-12
Published online: 2019-04-01

DOI: 10.1016/j.crma.2019.04.005

Author's affiliations:

Yong Han ¹; Yuefei Wang ²; Michel Zinsmeister ³

¹ Yau Mathematical Sciences Center, Tsinghua University, Beijng, 100084, China
² Institute of Mathematics, Academy of Mathematics and Systems Sciences and University of the Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100190, China
³ IDP, Université d'Orléans, BP 6759, 45067 Orléans cedex 2, France

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     author = {Yong Han and Yuefei Wang and Michel Zinsmeister},
     title = {SLE intersecting with random hulls},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {395--400},
     publisher = {Elsevier},
     volume = {357},
     number = {4},
     year = {2019},
     doi = {10.1016/j.crma.2019.04.005},
     language = {en},
}

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Yong Han; Yuefei Wang; Michel Zinsmeister. SLE intersecting with random hulls. Comptes Rendus. Mathématique, Volume 357 (2019) no. 4, pp. 395-400. doi : 10.1016/j.crma.2019.04.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.04.005/

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Cited by

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