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:**

- 60K35 Interacting random processes; statistical mechanics type models; percolation theory, See also {82B43, 82C43}
- 60G42 Martingales with discrete parameter
- 82C44 Dynamics of disordered systems (random Ising systems, etc.)
- 82D30 Random media, disordered materials (including liquid crystals and spin glasses)

**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