A Study in Markov Chains, Loop-Erased Random Walk and Loop Soups
Probability
2024-11-18 v1
Abstract
In this paper, we make a few random explorations that relate directly to the items mentioned in the title. We define transient chains and recurrent chains with "killing", the Green's function, the Laplacian operator, and harmonic functions. We then introduce the loop-erased random walk (LERW) and its relationship with the uniform spanning tree (UST). We finish by introducing loop measures and soups and defining the "growing loop" model.
Cite
@article{arxiv.2411.09988,
title = {A Study in Markov Chains, Loop-Erased Random Walk and Loop Soups},
author = {Zhuohan Gu},
journal= {arXiv preprint arXiv:2411.09988},
year = {2024}
}