# Convergence of the law of the Environment Seen by the Particle for Directed Polymers in Random Media in the $L^2$ region

Abstract : We consider the model of Directed Polymers in an i.i.d. gaussian or bounded Environment in the $L^2$ region. We prove the convergence of the law of the environment seen by the particle. As a main technical step, we establish a lower tail concentration inequality for the partition function for bounded environments. Our proof is based on arguments developed by Talagrand in the context of the Hopfield Model. This improves in some sense a concentration inequality obtained by Carmona and Hu for gaussian environments. We use this and a Local Limit Theorem to prove the $L^1$ convergence of the density of the law of the environment seen by the particle with respect to the product measure.
Keywords :
Type de document :
Pré-publication, Document de travail
2008
Domaine :

https://hal.archives-ouvertes.fr/hal-00294613
Contributeur : Gregorio Moreno Flores <>
Soumis le : jeudi 11 décembre 2008 - 09:27:05
Dernière modification le : jeudi 27 avril 2017 - 09:46:30
Document(s) archivé(s) le : mercredi 22 septembre 2010 - 10:46:15

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MorenoFlores-decembre.pdf
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### Identifiants

• HAL Id : hal-00294613, version 2
• ARXIV : 0807.1685

### Citation

Gregorio Moreno Flores. Convergence of the law of the Environment Seen by the Particle for Directed Polymers in Random Media in the $L^2$ region. 2008. <hal-00294613v2>

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