- 02-41 Francis Comets, Tokuzo Shiga, Nobuo Yoshida
- Directed Polymers in Random Environment:
Path Localization and Strong Disorder
(46K, LaTex2e)
Jan 29, 02
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Abstract. We consider directed polymers in random environment.
Under mild assumptions on the environment, we prove here:
(i) equivalence of decay rate of the partition
function with some natural localization properties
of the path, (ii) quantitative estimates of the decay
of the partition function in dimensions one or two,
or at sufficiently low temperature,
(iii) existence of quenched free energy.
In particular, we generalize to general environments,
some of the results recently obtained by
P. Carmona and Y. Hu for a Gaussian environment.
We do not discuss here superdiffusivity or critical exponents.
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