publication . Preprint . Other literature type . Article . 2007

Random walk loop soup

Gregory F. Lawler; José A. Trujillo Ferreras;
Open Access English
  • Published: 01 Feb 2007
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.
Subjects
arXiv: Mathematics::Probability
free text keywords: Mathematics - Probability, Applied Mathematics, General Mathematics, Approximation theory, Brownian motion, Topology, Conformal symmetry, Random walk, Mathematical analysis, Mathematics, Brownian bridge
Related Organizations

[1] R. Bass (1995). Probabilistic Techniques in Analysis, Springer-Verlag.

[2] J. Koml´os, P. Major, and G. Tusn´ady (1975). An approximation of partial sums of independent RV's and the sample DF. I., Z. Wahr. 32, 111-131.

[3] G. Lawler and W. Werner (2004). The Brownian loop soup, Prob. Theor. Rel. Fields 128, 565-588.

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