Bridge Decomposition of Restriction Measures |
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Authors: | Tom Alberts and Hugo Duminil-Copin |
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Institution: | (1) Department of Physics and Astronomy, University of Aarhus, Aarhus, Denmark;(2) Niels Bohr Institute, Copenhagen, Denmark; |
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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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