Strong disorder implies strong localization for directed polymers in a random environment

Philippe Carmona (1) , Yueyun Hu (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 LAGA - Laboratoire Analyse, Géométrie et Applications

In this note we show that in any dimension $d$, the strong disorder property implies the strong localization property. This is established for a continuous time model of directed polymers in a random environment : the parabolic Anderson Model.

Mots clés: directed polymer; random environment; localization; Anderson

Domaines: Probabilités [math.PR]

Philippe Carmona, Yueyun Hu. Strong disorder implies strong localization for directed polymers in a random environment. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2006, 2, pp.217--229. ⟨hal-00018048v2⟩