LAST PASSAGE PERCOLATION AND TRAVELING FRONTS

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 Lévy process in this case. The case of bounded jumps yields a completely different behavior.
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https://hal.archives-ouvertes.fr/hal-00677712
Contributor : Francis Comets <>
Submitted on : Wednesday, January 30, 2013 - 9:04:16 PM
Last modification on : Tuesday, August 13, 2019 - 2:30:11 PM
Long-term archiving on: Monday, June 17, 2013 - 5:48:31 PM

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  • HAL Id : hal-00677712, version 3
  • ARXIV : 1203.2368

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Francis Comets, Jeremy Quastel, Alejandro F. Ramirez. LAST PASSAGE PERCOLATION AND TRAVELING FRONTS. 2013. ⟨hal-00677712v3⟩

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