Article

Last passage percolation and traveling fronts

03/2012;
Source: arXiv

ABSTRACT We consider a system of N particles with a stochastic dynamics introduced by
Brunet and Derrida. The particles can be interpreted as last passage times in
directed percolation on {1,...,N} of mean-field type. The particles remain
grouped and move like a traveling wave, subject to discretization and driven by
a random noise. As N increases, we obtain estimates for the speed of the front
and its profile, for different laws of the driving noise. The Gumbel
distribution plays a central role for the particle jumps, and we show that the
scaling limit is a L\'evy process in this case. The case of bounded jumps
yields a completely different behavior.

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Keywords

central role
 
different laws
 
driving noise
 
last passage times
 
mean-field type
 
N increases
 
random noise
 
scaling limit
 
stochastic dynamics
 
traveling wave