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Abstract: The long-time-large-scale, small-friction asymptotic for the one dimensionalLangevin equation with a periodic potential is studied in this paper. It isshown that the Freidlin-Wentzell and central limit theorem homogenizationlimits commute. We prove that, in the combined small friction,long-time-large-scale limit the particle position converges weakly to aBrownian motion with a singular diffusion coefficient which we computeexplicitly. We show that the same result is valid for a whole one parameterfamily of space-time rescalings. The proofs of our main results are based onsome novel estimates on the resolvent of a hypoelliptic operator.



Author: Martin Hairer, Grigorios Pavliotis

Source: https://arxiv.org/







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