Majorizing multiplicative cascades for directed polymers in random media

Francis Comets (1) , Vincent Vargas (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

In this note we give upper bounds for the free energy of discrete polymers in random media. The bounds are given by the so-called generalized multiplicative cascades from the statistical theory of turbulence. For the polymer model, we derive that the quenched free energy is different from the annealed one in dimension 1, for any finite temperature and general environment. This implies localization of the polymer.

Mots clés: Directed polymers; random environment

Domaines: Probabilités [math.PR]

Francis Comets, Vincent Vargas. Majorizing multiplicative cascades for directed polymers in random media. 2005. ⟨hal-00012577⟩