publication . Other literature type . Preprint . Article . 2004

The Brownian loop soup

Gregory F. Lawler; Wendelin Werner;
Open Access
  • Published: 01 Apr 2004
  • Publisher: Springer Science and Business Media LLC
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.
Subjects
free text keywords: Mathematics - Probability, Statistics, Probability and Uncertainty, Statistics and Probability, Analysis, Mathematical analysis, Brownian motion, Invariant measure, Boundary (topology), Probability theory, A domain, Conformal symmetry, Mathematics, Mathematical finance, Schramm–Loewner evolution

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