A homogenization theorem for langevin systems with an application to hamiltonian dynamics

Jeremiah Birrell, Jan Wehr

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

This paper studies homogenization of stochastic differential systems. The standard example of this phenomenon is the small mass limit of Hamiltonian systems. We consider this case first from the heuristic point of view, stressing the role of detailed balance and presenting the heuristics based on a multiscale expansion. This is used to propose a physical interpretation of recent results by the authors, as well as to motivate a new theorem proven here. Its main content is a sufficient condition, expressed in terms of solvability of an associated partial differential equation (“the cell problem”), under which the homogenization limit of an SDE is calculated explicitly. The general theorem is applied to a class of systems, satisfying a generalized detailed balance condition with a position-dependent temperature.

Original languageEnglish (US)
Title of host publicationSojourns in Probability Theory and Statistical Physics - I - Spin Glasses and Statistical Mechanics, A Festschrift for Charles M. Newman
EditorsVladas Sidoravicius
PublisherSpringer
Pages89-122
Number of pages34
ISBN (Print)9789811502934
DOIs
StatePublished - Jan 1 2019
EventInternational Conference on Probability Theory and Statistical Physics, 2016 - Shanghai, China
Duration: Mar 25 2016Mar 27 2016

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume298
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational Conference on Probability Theory and Statistical Physics, 2016
CountryChina
CityShanghai
Period3/25/163/27/16

Keywords

  • Hamiltonian system
  • Homogenization
  • Noise-induced drift
  • Small mass limit
  • Stochastic differential equation

ASJC Scopus subject areas

  • Mathematics(all)

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