Bernoulli

Directed polymers in a random environment: path localization and strong disorder

Abstract

We consider directed polymers in a random environment. Under some mild assumptions on the environment, we prove equivalence between the decay rate of the partition function and some natural localization properties of the path; some quantitative estimates of the decay of the partition function in one or two dimensions, or at sufficiently low temperature; and the existence of quenched free energy. In particular, we generalize to general environments the results recently obtained by Carmona and Hu for a Gaussian environment. Our approach is based on martingale decomposition and martingale analysis. It leads to a natural, asymptotic relation between the partition function, and the probability that two polymers in the same environment, but otherwise independent, end up at the same point.

Article information

Source
Bernoulli Volume 9, Number 4 (2003), 705-723.

Dates
First available: 15 October 2003

http://projecteuclid.org/euclid.bj/1066223275

Mathematical Reviews number (MathSciNet)
MR1996276

Zentralblatt MATH identifier
02072459

Digital Object Identifier
doi:10.3150/bj/1066223275

Citation

Comets, Francis; Shiga, Tokuzo; Yoshida, Nobuo. Directed polymers in a random environment: path localization and strong disorder. Bernoulli 9 (2003), no. 4, 705--723. doi:10.3150/bj/1066223275. http://projecteuclid.org/euclid.bj/1066223275.