Schramm's formula for multiple loop-erased random walks
Statistical Mechanics
2018-11-05 v2 Mathematical Physics
math.MP
Abstract
We revisit the computation of the discrete version of Schramm's formula for the loop-erased random walk derived by Kenyon. The explicit formula in terms of the Green function relies on the use of a complex connection on a graph, for which a line bundle Laplacian is defined. We give explicit results in the scaling limit for the upper half-plane, the cylinder and the Moebius strip. Schramm's formula is then extended to multiple loop-erased random walks.
Keywords
Cite
@article{arxiv.1801.03126,
title = {Schramm's formula for multiple loop-erased random walks},
author = {Adrien Poncelet},
journal= {arXiv preprint arXiv:1801.03126},
year = {2018}
}
Comments
59 pages, 19 figures. v2: reformulation of Section 2.3, minor corrections