SLE intersecting with random hulls. (Intersection de SLE avec une enveloppe aléatoire.) (English. French summary) Zbl 1412.60119
Summary: G. Lawler et al. [J. Am. Math. Soc. 16, No. 4, 917–955 (2003; Zbl 1030.60096)] gave in 2003 an explicit formula of the probability that \(\operatorname{SLE}(8 / 3)\) does not intersect a deterministic hull. For general \(\operatorname{SLE}(\kappa)\) with \(\kappa \neq 8 / 3\), 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 \(\operatorname{SLE}(\kappa)\) does not intersect this random hull for any \(\kappa \in(0, 8)\). As a corollary, we will give a new proof of Werner’s result on conformal restriction measures.
MSC:
| 60J65 | Brownian motion |
Citations:
Zbl 1030.60096References:
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