Very Strong Disorder for the Parabolic Anderson model in low dimensions

Pierre Bertin (1, 2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We study the free energy of the Parabolic Anderson Model, a time-continuous model of directed polymers in random environment. We prove that in dimension 1 and 2, the free energy is always negative, meaning that very strong disorder always holds. The result for discrete polymers in dimension two, as well as better bounds on the free energy on dimension 1, were first obtained by Hubert Lacoin, and the goal of this paper is to adapt his proof to the Anderson Parabolic Model.

Mots clés: Coarse graining; Parabolic Anderson model; Brownian Directed Polymer; Free energy; Strong disorder; Coarse graining.

Domaines: Probabilités [math.PR]

Pierre Bertin. Very Strong Disorder for the Parabolic Anderson model in low dimensions. 2012. ⟨hal-00766752⟩