Imperial College London

Professor Grigorios A. Pavliotis

Faculty of Natural SciencesDepartment of Mathematics

Professor of Applied Mathematics



+44 (0)20 7594 8564g.pavliotis Website




736aHuxley BuildingSouth Kensington Campus






BibTex format

author = {Hairer, M and Pavliotis, GA},
doi = {10.1007/s10955-008-9493-3},
journal = {Journal of Statistical Physics},
pages = {175--202},
title = {From ballistic to diffusive behavior in periodic potentials},
url = {},
volume = {131},
year = {2008}

RIS format (EndNote, RefMan)

AB - 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.
AU - Hairer,M
AU - Pavliotis,GA
DO - 10.1007/s10955-008-9493-3
EP - 202
PY - 2008///
SN - 1572-9613
SP - 175
TI - From ballistic to diffusive behavior in periodic potentials
T2 - Journal of Statistical Physics
UR -
UR -
UR -
VL - 131
ER -