LAST PASSAGE PERCOLATION AND TRAVELING WAVES

Francis Comets (1) , Jeremy Quastel (2) , Alejandro F. Ramirez (3)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 Department of Mathematics [University of Toronto]
3 Departamento de Matemáticas [Santiago de Chile]

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.

Mots clés: Front propagation; Last passage percolation; Traveling wave; Interacting Particle Systems; Front propagation.

Domaines: Probabilités [math.PR]

Francis Comets, Jeremy Quastel, Alejandro F. Ramirez. LAST PASSAGE PERCOLATION AND TRAVELING WAVES. 2012. ⟨hal-00677712v1⟩