Abstract
We study the asymptotic behavior of the free energy for a model (defined by Sinai) of one-dimensional random walk with random potential. In particular, we obtain a central limit theorem and a strong law of large numbers for this free energy. We use some results on the free energy to study some sample path properties of this random walk which are related respectively to its recurrence and localization. Some exponents describing the recurrence and localization are found.
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Albeverio, S., Zhou, X.Y. Free energy and some sample path properties of a random walk with random potential. J Stat Phys 83, 573–622 (1996). https://doi.org/10.1007/BF02183741
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DOI: https://doi.org/10.1007/BF02183741