Directed Polymers in Random Environment are Diffusive at Weak Disorder

Francis Comets (1) , Nobuo Yoshida (2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 Division of Mathematics

In this paper, we consider directed polymers in random environment with discrete space and time. For transverse dimension at least equal to 3, we prove that diffusivity holds for the path in the full weak disorder region, i.e., where the partition function differs from its annealed value only by a non-vanishing factor. Deep inside this region, we also show that the quenched averaged energy has fluctuations of order 1. In complete generality (arbitrary dimension and temperature), we prove monotonicity of the phase diagram in the temperature.

Mots clés: Directed polymers; random environment; weak disorder; diffusive behavior; invariance principle; FKG inequality

Domaines: Probabilités [math.PR]

Francis Comets, Nobuo Yoshida. Directed Polymers in Random Environment are Diffusive at Weak Disorder. 2005. ⟨hal-00003250v2⟩