Scientific article
English

Bridge Decomposition of Restriction Measures

Published inJournal of statistical physics, vol. 140, no. 3, p. 467-493
Publication date2010
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 Itô's excursion decomposition of a Brownian motion according to its zeros.

Keywords
  • Self-avoiding walk
  • Conformal invariance
  • SLE
  • Restriction measures
  • Poisson process
  • Excursion theory
Citation (ISO format)
ALBERTS, Tom, DUMINIL-COPIN, Hugo. Bridge Decomposition of Restriction Measures. In: Journal of statistical physics, 2010, vol. 140, n° 3, p. 467–493. doi: 10.1007/s10955-010-9999-3
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Article (Published version)
accessLevelRestricted
Identifiers
Journal ISSN0022-4715
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