The Brownian loop soup

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.Cornell University; Research supported in part by the National Science FoundationUniversité Paris-Sud and IUFMathematics Subject Classification (2000):60J65, 81T40