3 research outputs found
New bounds for the free energy of directed polymers in dimension 1+1 and 1+2
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.Comment: 31 pages, 4 figures, final version, accepted for publication in
Communications in Mathematical Physic