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The Brownian loop soup

Gregory F. Lawler·Wendelin Werner
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Abstract

We define a natural conformally invariant measure on unrooted Brownian loops in the plane and study some of its properties. We relate this measure to a measure on loops rooted at a boundary point of a domain and show how this relation gives a way to ``chronologically add Brownian loops'' to simple curves in the plane.

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Gregory F. Lawler, Wendelin Werner. 2003-04-26. The Brownian loop soup. https://arxiv.org/abs/math/0304419

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