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- Title
From Ballistic to Diffusive Behavior in Periodic Potentials.
- Authors
Hairer, M.; Pavliotis, G. A.
- Abstract
The long-time/large-scale, small-friction asymptotic for the one dimensional Langevin equation with a periodic potential is studied in this paper. It is shown that the Freidlin-Wentzell and central limit theorem (homogenization) limits commute. We prove that, in the combined small friction, long-time/large-scale limit the particle position converges weakly to a Brownian motion with a singular diffusion coefficient which we compute explicitly. We show that the same result is valid for a whole one parameter family of space/time rescalings. The proofs of our main results are based on some novel estimates on the resolvent of a hypoelliptic operator.
- Subjects
LANGEVIN equations; CENTRAL limit theorem; WIENER processes; HYPOELLIPTIC operators; STOCHASTIC differential equations
- Publication
Journal of Statistical Physics, 2008, Vol 131, Issue 1, p175
- ISSN
0022-4715
- Publication type
Article
- DOI
10.1007/s10955-008-9493-3