The Brownian loop soup

Gregory F. Lawler, Wendelin Werner

Published 2003-04-26Version 1

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.