Hairer, MartinPavliotis, G. A.2024-09-172024-09-172024-09-112008-04-0110.1007/s10955-008-9493-3https://infoscience.epfl.ch/handle/20.500.14299/241153WOS:000253522400009The 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.enNONEQUILIBRIUM STATISTICAL-MECHANICSSMOLUCHOWSKI-KRAMERS APPROXIMATIONFOKKER-PLANCK EQUATIONRANDOM PERTURBATIONSANHARMONIC CHAINSUHLENBECK PROCESSHOMOGENIZATIONOSCILLATORSEQUILIBRIUMTRANSPORThomogenizationhypoelliptic diffusionhypocoercivityScience & TechnologyPhysical Sciencestext::journal::journal article