Exact results on Sinai's diffusion

1998/09/07 by Alain Comtet, David S. Dean · 4 citations
Physics and Astronomy · #Spectroscopy and Quantum Chemical Studies #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat

paper · pdf · doi:10.1088/0305-4470/31/43/004

published as J. Phys. A. 31, 8595 (1998). · 14 pages Latex. To appear J. Phys. A

arxiv created 1998/09/07 · openalex publication_date 1998/10/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

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 representation 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.

Citations

• Nonequilibrium dynamics of spin glasses

Cited by

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