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 | References | Similar Articles | Additional Information

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

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.