Arkiv för Matematik

  • Ark. Mat.
  • Volume 50, Number 2 (2012), 331-357.

On the scaling limit of loop-erased random walk excursion

Fredrik Johansson Viklund

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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.

Article information

Source
Ark. Mat., Volume 50, Number 2 (2012), 331-357.

Dates
Received: 29 June 2010
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907176

Digital Object Identifier
doi:10.1007/s11512-011-0149-1

Mathematical Reviews number (MathSciNet)
MR2961326

Zentralblatt MATH identifier
1255.60176

Rights
2011 © Institut Mittag-Leffler

Citation

Johansson Viklund, Fredrik. On the scaling limit of loop-erased random walk excursion. Ark. Mat. 50 (2012), no. 2, 331--357. doi:10.1007/s11512-011-0149-1. https://projecteuclid.org/euclid.afm/1485907176


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