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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Random walk loop soup
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by Gregory F. Lawler and José A. Trujillo Ferreras PDF
Trans. Amer. Math. Soc. 359 (2007), 767-787 Request permission

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
  • MR Author ID: 111050
  • 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
  • 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
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 359 (2007), 767-787
  • MSC (2000): Primary 60G15, 60J65, 82B41
  • DOI: https://doi.org/10.1090/S0002-9947-06-03916-X
  • MathSciNet review: 2255196