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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Cornell University; Research supported in part by the National Science Foundation
Université Paris-Sud and IUF
Mathematics Subject Classification (2000): 60J65, 81T40
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Lawler, G., Werner, W. The Brownian loop soup. Probab. Theory Relat. Fields 128, 565–588 (2004). https://doi.org/10.1007/s00440-003-0319-6
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DOI: https://doi.org/10.1007/s00440-003-0319-6