Last Passage Percolation and Traveling Waves

Details Last Passage Percolation and Traveling Waves Last Passage Percolation and Traveling Waves

2012-03-11

arxiv.org/abs/1203.2368v1

Mathematics

Probability

Scientific paper

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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