Directed Polymers in Random Environment are Diffusive at Weak Disorder

Details Directed Polymers in Random Environment are Diffusive at Weak Disorder Directed Polymers in Random Environment are Diffusive at Weak Disorder

2004-11-10

arxiv.org/abs/math/0411223v2

Mathematics

Probability

Scientific paper

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.

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