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.
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Research of Tom Alberts supported in part by NSF Grant OISE 0730136, and a postdoctoral fellowship from the Natural Sciences and Engineering Research Council of Canada. Research of Hugo Duminil-Copin supported in part by project MRTN-CT-2006-035651, Acronym CODY, of the European Commission, and a grant from the Swiss National Science Foundation.
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Alberts, T., Duminil-Copin, H. Bridge Decomposition of Restriction Measures. J Stat Phys 140, 467–493 (2010). https://doi.org/10.1007/s10955-010-9999-3
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DOI: https://doi.org/10.1007/s10955-010-9999-3