%0 Journal Article
%T Last passage percolation and traveling fronts
%A Francis Comets
%A Jeremy Quastel
%A Alejandro F. Ramirez
%J Mathematics
%D 2012
%I arXiv
%R 10.1007/s10955-013-0779-8
%X 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.
%U http://arxiv.org/abs/1203.2368v3