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Random walk loop soup | | Gregory F. Lawler
; José A. Trujillo Ferreras
; | | Date: |
16 Sep 2004 | | Subject: | Probability | math.PR | | Affiliation: | Cornell University), José A. Trujillo Ferreras (Cornell University | | 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 Komlós, Major, and Tusnády. To make the paper self-contained, we include a proof of the approximation result that we need. | | Source: | arXiv, math.PR/0409291 | | Services: | Forum | Review | PDF | Favorites | |
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