7,491 research outputs found
Branching Brownian Motion with catalytic branching at the origin
We consider a branching Brownian motion in which binary fission takes place
only when particles are at the origin at a rate \beta > 0 on the local time
scale. We obtain results regarding the asymptotic behaviour of the number of
particles above \lambda t at time t, for \lambda > 0. As a corollary, we
establish the almost sure asymptotic speed of the rightmost particle. We also
prove a Strong Law of Large Numbers for this catalytic branching Brownian
motion.Comment: 25 page
Growth rates of the population in a branching Brownian motion with an inhomogeneous breeding potential
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 , for . 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.Comment: 56 pages, 1 figur
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