Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Strong disorder for a certain class of directed polymers in a random environment

Auteur(s):

Code(s) de Classification MSC:

• 60K37 Processes in random environments

Résumé: We study a model of directed polymers in a random environment with a positive recurrent Markov chain, taking values in a countable space $\Sigma$. The random environment is a family $(g(i,x), i \geq 1, x \in \Sigma)$ of independent and identically distributed real-valued variables. The asymptotic behaviour of the normalized partition function is characterized: when the common law of the $g(.,.)$ is infinitely divisible and the Markov chain is exponentially recurrent we prove that the normalized partition function converges exponentially fast towards zero at all temperatures.

Mots Clés: Directed polymers ; random environment ; strong disorder

Date: 2004-03-24

Prépublication numéro: PMA-896