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Directed polymers in random environment are diffusive at weak disorder. (English) Zbl 1104.60061
Summary: 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, that is, where the partition function differs from its annealed value only by a nonvanishing 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.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60G42 Martingales with discrete parameter
82D30 Statistical mechanical studies of random media, disordered materials (including liquid crystals and spin glasses)
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