Advertisement

Communications in Mathematical Physics

, Volume 104, Issue 1, pp 1–19 | Cite as

Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions

  • C. Kipnis
  • S. R. S. Varadhan
Article

Abstract

We prove a functional central limit theorem for additive functionals of stationary reversible ergodic Markov chains under virtually no assumptions other than the necessary ones. We use these results to study the asymptotic behavior of a tagged particle in an infinite particle system performing simple excluded random walk.

Keywords

Neural Network Statistical Physic Complex System Markov Chain Asymptotic Behavior 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arratia, R.: The motion of a tagged particle in the simple symmetric exclusion system in Z. Ann. Probab.11 362–373 (1983)Google Scholar
  2. 2.
    Helland, I.: Central limit theorems for martingales with discrete or continuous time. Scand. J. Stat.,9, 79–94 (1982)Google Scholar
  3. 3.
    Kipnis, C., Lebowitz, J. L., Presutti, E., Spohn, H.: J. Stat. Phys.30, 107–121 (1983)Google Scholar
  4. 4.
    Lebowitz, J. L., Spohn, H.: J. Stat. Phys.28, 539–556 (1982)Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • C. Kipnis
    • 1
  • S. R. S. Varadhan
    • 2
  1. 1.Centre de Mathematiques AppliqueésEcole PolytechniquePalaiseauFrance
  2. 2.Courant InstituteNew York UniversityNew YorkUSA

Personalised recommendations