Convergence of the law of the Environment Seen by the Particle for Directed Polymers in Random Media in the $L^2$ region - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2008

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

Résumé

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.
Fichier principal
Vignette du fichier
MorenoFlores.pdf (172.77 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00294613 , version 1 (09-07-2008)
hal-00294613 , version 2 (11-12-2008)

Identifiants

Citer

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-00294613v1⟩
206 Consultations
241 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More