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.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
- 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