Lawler, Schramm, and Werner gave in 2003 an explicit formula of the probability that does not intersect a deterministic hull. For general with , 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 does not intersect this random hull for any . 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 ne rencontre pas une enveloppe déterministe. Pour avec , 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 ne la rencontre pas lorsque . Comme corollaire, nous donnons une nouvelle démonstration d'un résultat de Werner sur les mesures de restrictions conformes.
Accepted:
Published online:
Yong Han 1; Yuefei Wang 2; Michel Zinsmeister 3
@article{CRMATH_2019__357_4_395_0, 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}, }
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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