New bounds for the free energy of directed polymers in dimension 1+1 and 1+2

Details New bounds for the free energy of directed polymers in dimension 1+1 and 1+2 New bounds for the free energy of directed polymers in dimension 1+1 and 1+2

2009-01-06

arxiv.org/abs/0901.0699v3

Physics

Mathematical Physics

31 pages, 4 figures, final version, accepted for publication in Communications in Mathematical Physics

Scientific paper

We study the free energy of the directed polymer in random environment in dimension 1+1 and 1+2. For dimension 1, we improve the statement of Comets and Vargas concerning very strong disorder by giving sharp estimates on the free energy at high temperature. In dimension 2, we prove that very strong disorder holds at all temperatures, thus solving a long standing conjecture in the field.

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