Directed polymers in a random environment: path localization and strong disorder
Comets, Francis ; Shiga, Tokuzo ; Yoshida, Nobuo
Bernoulli, Tome 9 (2003) no. 3, p. 705-723 / Harvested from Project Euclid
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.
Publié le : 2003-08-14
Classification:  directed polymers,  martingales,  random environment
@article{1066223275,
     author = {Comets, Francis and Shiga, Tokuzo and Yoshida, Nobuo},
     title = {Directed polymers in a random environment: path localization and strong disorder},
     journal = {Bernoulli},
     volume = {9},
     number = {3},
     year = {2003},
     pages = { 705-723},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1066223275}
}
Comets, Francis; Shiga, Tokuzo; Yoshida, Nobuo. Directed polymers in a random environment: path localization and strong disorder. Bernoulli, Tome 9 (2003) no. 3, pp.  705-723. http://gdmltest.u-ga.fr/item/1066223275/