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

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