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Title

Bridge Decomposition of Restriction Measures

Authors
Alberts, Tom
Published in Journal of Statistical Physics. 2010, vol. 140, no. 3, p. 467 - 493
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 walkConformal invarianceSLERestriction measuresPoisson processExcursion theory
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ALBERTS, Tom, DUMINIL-COPIN, Hugo. Bridge Decomposition of Restriction Measures. In: Journal of Statistical Physics, 2010, vol. 140, n° 3, p. 467 - 493. https://archive-ouverte.unige.ch/unige:11943

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Deposited on : 2010-09-28

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