Transition probabilities for infinite two-sided loop-erased random walks
Probability
2019-11-20 v2
Abstract
The infinite two-sided loop-erased random walk (LERW) is a measure on infinite self-avoiding walks that can be viewed as giving the law of the `middle part' of an infinite LERW loop going through 0 and infinity. In this note we derive expressions for transition probabilities for this model in dimensions two and up. In the plane, the formula can be further expressed in terms of a Laplacian with signed weights acting on certain discrete harmonic functions at the tips of the walk, and taking a determinant. The discrete harmonic functions are closely related to a discrete version of the complex square-root.
Cite
@article{arxiv.1810.08593,
title = {Transition probabilities for infinite two-sided loop-erased random walks},
author = {Christian Beneš and Gregory F. Lawler and Fredrik Viklund},
journal= {arXiv preprint arXiv:1810.08593},
year = {2019}
}
Comments
21 pages. Minor corrections in second version