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On the scaling limit of loop-erased random walk excursion

Fredrik Johansson Viklund Department of Mathematics, Columbia University

Complex Variables and Complex Analysis Probability mathscidoc:1701.08007

Arkiv for Matematik, 50, (2), 331-357, 2010.6
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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@inproceedings{fredrik2010on,
  title={On the scaling limit of loop-erased random walk excursion},
  author={Fredrik Johansson Viklund},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203632970987024},
  booktitle={Arkiv for Matematik},
  volume={50},
  number={2},
  pages={331-357},
  year={2010},
}
Fredrik Johansson Viklund. On the scaling limit of loop-erased random walk excursion. 2010. Vol. 50. In Arkiv for Matematik. pp.331-357. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203632970987024.
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