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October 2012 On the scaling limit of loop-erased random walk excursion
Fredrik Johansson Viklund
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Ark. Mat. 50(2): 331-357 (October 2012). DOI: 10.1007/s11512-011-0149-1

Abstract

We use the known convergence of loop-erased random walk to radial SLE(2) to give a new proof that the scaling limit of loop-erased random walk excursion in the upper half-plane is chordal SLE(2). Our proof relies on a version of Wilson’s algorithm for weighted graphs which is used together with a Beurling-type estimate for random walk excursion. We also establish and use the convergence of the radial SLE path to the chordal SLE path as the bulk point tends to a boundary point. In the final section we sketch how to extend our results to more general simply connected domains.

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Fredrik Johansson Viklund. "On the scaling limit of loop-erased random walk excursion." Ark. Mat. 50 (2) 331 - 357, October 2012. https://doi.org/10.1007/s11512-011-0149-1

Information

Received: 29 June 2010; Published: October 2012
First available in Project Euclid: 31 January 2017

zbMATH: 1255.60176
MathSciNet: MR2961326
Digital Object Identifier: 10.1007/s11512-011-0149-1

Rights: 2011 © Institut Mittag-Leffler

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Vol.50 • No. 2 • October 2012
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