The Brownian loop soup

Details The Brownian loop soup The Brownian loop soup

2003-04-26

arxiv.org/abs/math/0304419v1

Mathematics

Probability

Scientific paper

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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