%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