Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10527338 | Stochastic Processes and their Applications | 2015 | 50 Pages |
Abstract
We consider a branching particle system where each particle moves as an independent Brownian motion and breeds at a rate proportional to its distance from the origin raised to the power p, for pâ[0,2). The asymptotic behaviour of the right-most particle for this system is already known; in this article we give large deviations probabilities for particles following “difficult” paths, growth rates along “easy” paths, the total population growth rate, and we derive the optimal paths which particles must follow to achieve this growth rate.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Julien Berestycki, Ãric Brunet, John W. Harris, Simon C. Harris, Matthew I. Roberts,