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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Random walk loop soup


Authors: Gregory F. Lawler and José A. Trujillo Ferreras
Journal: Trans. Amer. Math. Soc. 359 (2007), 767-787
MSC (2000): Primary 60G15, 60J65, 82B41
Published electronically: September 12, 2006
MathSciNet review: 2255196
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Abstract: The Brownian loop soup introduced by Lawler and Werner (2004) is a Poissonian realization from a $ \sigma$-finite measure on unrooted loops. This measure satisfies both conformal invariance and a restriction property. In this paper, we define a random walk loop soup and show that it converges to the Brownian loop soup. In fact, we give a strong approximation result making use of the strong approximation result of Komlós, Major, and Tusnády. To make the paper self-contained, we include a proof of the approximation result that we need.


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Additional Information

Gregory F. Lawler
Affiliation: Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853-4201
Email: lawler@math.cornell.edu

José A. Trujillo Ferreras
Affiliation: Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853-4201
Address at time of publication: Forschungsinstitut für Mathematik, ETH-Zentrum, HG G 44.1, CH-8092, Zürich, Switzerland
Email: jatf@math.cornell.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03916-X
PII: S 0002-9947(06)03916-X
Keywords: Brownian loop soup, dyadic approximation, Brownian bridge
Received by editor(s): October 26, 2004
Received by editor(s) in revised form: December 8, 2004
Published electronically: September 12, 2006
Additional Notes: The first author was supported by the National Science Foundation
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.