Front velocity and directed polymers in random medium

Aser Cortines

Stochastic Processes and their Applications, 2014, vol. 124, issue 11, 3698-3723

Abstract: We consider a stochastic model of N evolving particles studied by Brunet and Derrida. This model can be seen as a directed polymer in random medium with N sites in the transverse direction. Cook and Derrida use heuristic arguments to obtain a formula for the ground state energy of the polymer. We formalize their argument and show that there is an additional term in the formula in the critical case. We also consider a generalization of the model, and show that in the noncritical case the behavior is basically the same, whereas in the critical case a new correction appears.

Keywords: Interacting particle systems; Front propagation; Traveling wave; Directed polymer in random medium; Ground state (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1016/j.spa.2014.05.012

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