2004/05/05 by Julien Dubédat, Julien Dubedat · 3 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Brownian excursion #Brownian motion #Combinatorics #Computer science #Excursion #Geometric Brownian motion #Geometry #Mathematical economics #Mathematics #Percolation (cognitive psychology) #Property (philosophy) #Random Matrices and Applications #Rectangle #Statistics #Stochastic processes and statistical mechanics #math.PR #msc:60G18 #msc:60G51 #msc:60K35 #msc:82B43
paper · pdf · doi:10.1007/s00440-005-0446-3
published as Probab. Theory Related Fields 134 (2006), no. 3, 453--488 · 36 pages
arxiv created 2004/05/05 · openalex publication_date 2005/06/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.