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Abstract: Motivated by Kesten-s bridge decomposition for two-dimensional self-avoidingwalks in the upper half plane, we show that the conjectured scaling limit ofthe half-plane SAW, the SLE8-3 process, also has an appropriately definedbridge decomposition. This continuum decomposition turns out to entirely be aconsequence of the restriction property of SLE8-3, and as a result can begeneralized to the wider class of restriction measures. Specifically we showthat the restriction hulls with index less than one can be decomposed into aPoisson Point Process of irreducible bridges in a way that is similar to Ito-sexcursion decomposition of a Brownian motion according to its zeros.



Author: Tom Alberts, Hugo Duminil-Copin

Source: https://arxiv.org/







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