Excursion decompositions for $\SLE$ and Watts' crossing formula
| dc.creator | Dubedat, Julien | |
| dc.date | 2004-05-05 | |
| dc.date.accessioned | 2026-07-07T08:42:07Z | |
| dc.date.available | 2026-07-07T08:42:07Z | |
| dc.description | It is known that Schramm-Loewner Evolutions (SLEs) have a.s. frontier points if $κ>4$ and a.s. cutpoints if $4<κ<8$. If $κ>4$, an appropriate version of $\SLE(κ)$ has a renewal property: it starts afresh after visiting its frontier. Thus one can give an excursion decomposition for this particular $\SLE(κ)$ ``away from its frontier''. For $4<κ<8$, there is a two-sided analogue of this situation: a particular version of $\SLE(κ)$ has a renewal property w.r.t its cutpoints; one studies excursion decompositions of this $\SLE$ ``away from its cutpoints''. For $κ=6$, this overlaps Virág's results on ``Brownian beads''. As a by-product of this construction, one proves Watts' formula, which describes the probability of a double crossing in a rectangle for critical plane percolation. | |
| dc.description | 36 pages | |
| dc.identifier | https://arxiv.org/abs/math/0405074 | |
| dc.identifier | http://arxiv.org/abs/math/0405074 | |
| dc.identifier | Probab. Theory Related Fields 134 (2006), no. 3, 453--488 | |
| dc.identifier | doi:10.1007/s00440-005-0446-3 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141860 | |
| dc.subject | Probability | |
| dc.subject | 60K35; 82B43; 60G18; 60G51 | |
| dc.title | Excursion decompositions for $\SLE$ and Watts' crossing formula | |
| dc.type | text |