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A capture problem in Brownian motion and eigenvalues of spherical domains
Author(s):
Jesse
Ratzkin;
Andrejs
Treibergs
Journal:
Trans. Amer. Math. Soc.
361
(2009),
391-405.
MSC (2000):
Primary 60J65;
Secondary 35P15
Posted:
August 19, 2008
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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.
References:
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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:
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
Posted:
August 19, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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