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Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 1998

Exact Results on Sinai's Diffusion

Résumé

We study the continuum version of Sinai\'s problem of a random walker in a random force field in one dimension. A method of stochastic representations is used to represent various probability distributions in this problem (mean probability density function and first passage time distributions). This method reproduces already known rigorous results and also confirms directly some recent results derived using approximation schemes. We demonstrate clearly, in the Sinai scaling regime, that the disorder dominates the problem and that the thermal distributions tend to zero-one laws.

Dates et versions

hal-00003992 , version 1 (25-01-2005)

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Alain Comtet, David S. Dean. Exact Results on Sinai's Diffusion. Journal of Physics A: Mathematical and Theoretical, 1998, 31, pp.8595. ⟨hal-00003992⟩

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UNIV-PARIS-SACLAY
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