Bridge Decomposition of Restriction Measures
Abstract
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.
Cite
@article{arxiv.0909.0203,
title = {Bridge Decomposition of Restriction Measures},
author = {Tom Alberts and Hugo Duminil-Copin},
journal= {arXiv preprint arXiv:0909.0203},
year = {2010}
}
Comments
24 pages, 2 figures. Final version incorporates minor revisions suggested by the referee, to appear in Jour. Stat. Phys