Advanced Studies in Pure Mathematics

Probabilistic Analysis of Directed Polymers in a Random Environment: a Review

Francis Comets, Tokuzo Shiga, and Nobuo Yoshida

Full-text: Open access

Abstract

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].

Article information

Source
Stochastic Analysis on Large Scale Interacting Systems, T. Funaki and H. Osada, eds. (Tokyo: Mathematical Society of Japan, 2004), 115-142

Dates
Received: 28 March 2003
Revised: 10 June 2003
First available in Project Euclid: 1 January 2019

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1546369036

Digital Object Identifier
doi:10.2969/aspm/03910115

Mathematical Reviews number (MathSciNet)
MR2073332

Zentralblatt MATH identifier
1114.82017

Citation

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


Export citation