Random walk loop soup

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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 Komlós, Major, and Tusnády. To make the paper self-contained, we include a proof of the approximation result that we need.

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Probability

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http://salesiana.dossiersoluciones.com/handle/123456789/72503

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0409291
 http://arxiv.org/abs/math/0409291

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arXiv