Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Stochastic Analysis on Large Scale Interacting Systems, T. Funaki and H. Osada, eds. (Tokyo: Mathematical Society of Japan, 2004), 115 - 142
Probabilistic Analysis of Directed Polymers in a Random Environment: a Review
Directed polymers in random environment can be thought of as a model of statistical mechanics in which paths of stochastic processes interact with a quenched disorder (impurities), depending on both time and space. We review here main results which have been obtained during the last fifteen years, with proofs to most of the results. The material covers the diffusive behavior of the polymers in weak disorder phase studied by J. Imbrie, T. Spencer, E. Bolthausen, R. Song and X. Y. Zhou [11, 3, 25], and localization of the paths in strong disordered phase recently obtained by P. Carmona, Y. Hu, and the authors of the present article [4, 5].
Received: 28 March 2003
Revised: 10 June 2003
First available in Project Euclid: 1 January 2019
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Comets, Francis; Shiga, Tokuzo; Yoshida, Nobuo. Probabilistic Analysis of Directed Polymers in a Random Environment: a Review. Stochastic Analysis on Large Scale Interacting Systems, 115--142, Mathematical Society of Japan, Tokyo, Japan, 2004. doi:10.2969/aspm/03910115. https://projecteuclid.org/euclid.aspm/1546369036