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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48 .

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A capture problem in Brownian motion and eigenvalues of spherical domains
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by Jesse Ratzkin and Andrejs Treibergs PDF
Trans. Amer. Math. Soc. 361 (2009), 391-405 Request permission

Abstract:

We resolve a question of Bramson and Griffeath by showing that the expected capture time of four predators pursuing a single prey, all moving by standard Brownian motion on a line, is finite. Our main tool is an eigenvalue estimate for a particular spherical domain, which we obtain by a coning construction and domain perturbation.
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Additional Information
  • Jesse Ratzkin
  • Affiliation: Department of Mathematics, University of Connecticut, 196 Auditorium Road,Storrs, Connecticut 06269
  • Address at time of publication: Department of Mathematics, University of Georgia, Boyd Hall, Athens, Georgia 30602
  • Email: ratzkin@math.uconn.edu, jratzkin@math.uga.edu
  • Andrejs Treibergs
  • Affiliation: Department of Mathematics, University of Utah, 155 South 1400 East, JWB 233, Salt Lake City, Utah 84112
  • Received by editor(s): June 9, 2005
  • Received by editor(s) in revised form: February 21, 2007
  • Published electronically: August 19, 2008
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 361 (2009), 391-405
  • MSC (2000): Primary 60J65; Secondary 35P15
  • DOI: https://doi.org/10.1090/S0002-9947-08-04505-4
  • MathSciNet review: 2439411