Francis COMETS,Nobuo YOSHIDA
Directed Polymers in Random Environment are Diffusive 
at Weak Disorder
(208K, ps.gz)

ABSTRACT.  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.