English

The probability that planar loop-erased random walk uses a given edge

Probability 2013-01-24 v1

Abstract

We give a new proof of a result of Rick Kenyon that the probability that an edge in the middle of an n x n square is used in a loop-erased walk connecting opposites sides is of order n^{-3/4}. We, in fact, improve the result by showing that this estimate is correct up to multiplicative constants.

Keywords

Cite

@article{arxiv.1301.5331,
  title  = {The probability that planar loop-erased random walk uses a given edge},
  author = {Gregory F. Lawler},
  journal= {arXiv preprint arXiv:1301.5331},
  year   = {2013}
}
R2 v1 2026-06-21T23:13:47.910Z