Random walk loop soup

Details Random walk loop soup Random walk loop soup

2004-09-16

arxiv.org/abs/math/0409291v1

Mathematics

Probability

Scientific paper

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.

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