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Front velocity and directed polymers in random medium

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  • Cortines, Aser

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.

Suggested Citation

  • Cortines, Aser, 2014. "Front velocity and directed polymers in random medium," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3698-3723.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:11:p:3698-3723
    DOI: 10.1016/j.spa.2014.05.012
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