Random walk loop soup |
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Authors: | Gregory F Lawler José A Trujillo Ferreras |
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Institution: | Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853-4201 ; Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853-4201 |
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Abstract: | The Brownian loop soup introduced by Lawler and Werner (2004) is a Poissonian realization from a -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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Keywords: | Brownian loop soup dyadic approximation Brownian bridge |
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