Front velocity and directed polymers in random medium

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:124

Article

Cortines, Aser

关键词: Interacting particle systems;    Front propagation;    Traveling wave;    Directed polymer in random medium;    Ground state;   

DOI  :  10.1016/j.spa.2014.05.012

来源: Elsevier

【 摘 要 】

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. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free