Loop-erased random walk as a spin system observable
Probability
2020-09-02 v2 Mathematical Physics
math.MP
Abstract
The determination of the Hausdorff dimension of the scaling limit of loop-erased random walk is closely related to the study of the one-point function of loop-erased random walk, i.e., the probability a loop-erased random walk passes through a given vertex. Recent work in the theoretical physics literature has investigated the Hausdorff dimension of loop-erased random walk in three dimensions by applying field theory techniques to study spin systems that heuristically encode the one-point function of loop-erased random walk. Inspired by this, we introduce two different spin systems whose correlation functions can be rigorously shown to encode the one-point function of loop-erased random walk.
Cite
@article{arxiv.2003.10928,
title = {Loop-erased random walk as a spin system observable},
author = {Tyler Helmuth and Assaf Shapira},
journal= {arXiv preprint arXiv:2003.10928},
year = {2020}
}
Comments
Accepted version