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

 

A capture problem in Brownian motion and eigenvalues of spherical domains


Authors: Jesse Ratzkin and Andrejs Treibergs
Journal: Trans. Amer. Math. Soc. 361 (2009), 391-405
MSC (2000): Primary 60J65; Secondary 35P15
Published electronically: August 19, 2008
MathSciNet review: 2439411
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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

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04505-4
PII: S 0002-9947(08)04505-4
Received by editor(s): June 9, 2005
Received by editor(s) in revised form: February 21, 2007
Published electronically: August 19, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.