Directed Polymers in Random Environment: Path Localization and Strong Disorder
نویسندگان
چکیده
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. Short Title. Directed Polymers in Random Environment
منابع مشابه
Strong localization and macroscopic atoms for directed polymers
In this article, we derive strong localization results for directed polymers in random environment. We show that at ”low temperature” the polymer measure is asymptotically concentrated at a few points of macroscopic mass (we call these points ǫ-atoms). These results are derived assuming weak conditions on the tail decay of the random environment. MSC: 60K37;82B44
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