Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Directed Polymers in Random Environment: Path Localization and Strong Disorder


Code(s) de Classification MSC:

Résumé: We consider directed polymers in random environment. Under mild assumptions on the environment, we prove here: (i) equivalence of decay rate of the partition function with some natural localization properties of the path, (ii) quantitative estimates of the decay of the partition function in dimensions one or two, or at sufficiently low temperature, (iii) existence of quenched free energy. In particular, we generalize to general environments, some of the results recently obtained by P. Carmona and Y. Hu for a Gaussian environment. We do not discuss here superdiffusivity or critical exponents

Mots Clés: Directed polymers ; martingales ; random environment

Date: 2002-05-29

Prépublication numéro: PMA-732

Pdf file : PMA-732.pdf