Random walk loop soup
Probability
2007-05-23 v1
Abstract
The Brownian loop soup introduced in Lawler and Werner (2004) is a Poissonian realization from a sigma-finite measure on unrooted loops. This measure satisfies both conformal invariance and a restriction property. In this paper, we define a random walk loop soup and show that it converges to the Brownian loop soup. In fact, we give a strong approximation result making use of the strong approximation result of Koml\'os, Major, and Tusn\'ady. To make the paper self-contained, we include a proof of the approximation result that we need.
Keywords
Cite
@article{arxiv.math/0409291,
title = {Random walk loop soup},
author = {Gregory F. Lawler and José A. Trujillo Ferreras},
journal= {arXiv preprint arXiv:math/0409291},
year = {2007}
}