2009/09/30 by Tom Alberts, Hugo Duminil‐Copin, Hugo Duminil-Copin · 5 citations
Mathematics · Physics and Astronomy · #Brownian bridge #Brownian motion #Combinatorics #Decomposition #Geometry #Mathematical analysis #Mathematics #Physics #Plane (geometry) #Point process #Poisson point process #Pure mathematics #Random Matrices and Applications #Scaling #Scaling limit #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math-ph #math.MP #math.PR #msc:60K05 #msc:60K35 #msc:82B41
paper · pdf · doi:10.1007/s10955-010-9999-3
published in Journal of Statistical Physics 140(3), 467-493 (Springer Science+Business Media) · 24 pages, 2 figures. Final version incorporates minor revisions suggested by the referee, to appear in Jour. Stat. Phys
openalex publication_date 2010/06/04 · arxiv created 2010/07/03 · arxiv updated 2010/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Motivated by Kesten's bridge decomposition for two-dimensional self-avoiding walks in the upper half plane, we show that the conjectured scaling limit of the half-plane SAW, the SLE(8/3) process, also has an appropriately defined bridge decomposition. This continuum decomposition turns out to entirely be a consequence of the restriction property of SLE(8/3), and as a result can be generalized to the wider class of restriction measures. Specifically we show that the restriction hulls with index less than one can be decomposed into a Poisson Point Process of irreducible bridges in a way that is similar to Ito's excursion decomposition of a Brownian motion according to its zeros.