HAL: hal-00294613, version 2
 arXiv: 0807.1685
 Available versions: v1 (2008-07-10) v2 (2008-12-11)
 Convergence of the law of the Environment Seen by the Particle for Directed Polymers in Random Media in the $L^2$ region
 (2008-07-09)
 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.
 1: Laboratoire de Probabilités et Modèles Aléatoires (LPMA) CNRS : UMR7599 – Université Pierre et Marie Curie (UPMC) - Paris VI – Université Paris VII - Paris Diderot
 Subject : Mathematics/Probability
 Keyword(s): Directed polymers – Random media
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 hal-00294613, version 2 http://hal.archives-ouvertes.fr/hal-00294613 oai:hal.archives-ouvertes.fr:hal-00294613 From: Gregorio Moreno Flores <> Submitted on: Thursday, 11 December 2008 09:27:05 Updated on: Thursday, 11 December 2008 12:06:57