Hubert Lacoin
Published 2009-01-06, updated 2009-11-19Version 3
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.
Comments: 31 pages, 4 figures, final version, accepted for publication in Communications in Mathematical Physics
The high-temperature behavior for the directed polymer in dimension 1+2
Hausdorff and packing spectra, large deviations, and free energy for branching random walks in $\R^d$
The effect of disorder on the free-energy for the Random Walk Pinning Model: smoothing of the phase transition and low temperature asymptotics
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