laboratoire de physique statistique
 
 
laboratoire de physique statistique

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STOCHASTIC PROCESSES AND THEIR APPLICATIONS 


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2015
Growth rates of the population in a branching Brownian motion with an inhomogeneous breeding potential - Berestycki, Julien and Brunet, Eric and Harris, John W. and Harris, Simon C. and Roberts, Matthew I.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS 1252096-2145 (2015)

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 p is an element of [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. Crown Copyright (C) 2015 Published by Elsevier B.V.