Journal of Statistical Physics

, Volume 46, Issue 5–6, pp 1195–1232 | Cite as

Large deviations for noninteracting infinite-particle systems

  • M. D. Donsker
  • S. R. S. Varadhan
Articles

Abstract

A large deviation property is established for noninteracting infinite particle systems. Previous large deviation results obtained by the authors involved a singleI-function because the cases treated always involved a unique invariant measure for the process. In the context of this paper there is an infinite family of invariant measures and a corresponding infinite family ofI-functions governing the large deviations.

Key words

Large deviations infinite particle systems invariant measures asymptotics for expectations 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. D. Donsker and S. R. S. Varadhan, Asymptotic evaluation of certain Wiener integrals for large time, inFunctional Integration and Its Applications (Proceedings of the International Conference, London) (Clarendon Press, Oxford, 1975), pp. 15–33.Google Scholar
  2. 2.
    M. D. Donsker and S. R. S. Varadhan, Asymptotic evaluation of certain Wiener integrals for large time, I,Commun. Pure Appl. Math. 28:1–47 (1975); II,Commun. Pure Appl. Math. 28:279–301 (1975); III,Commun. Pure Appl. Math. 29:389–461 (1976); IV,Commun. Pure Appl. Math. 36:183–212 (1983).Google Scholar
  3. 3.
    M. D. Donsker and S. R. S. Varadhan, Large deviations for stationary Gaussian processes,Commun. Math. Phys. 97:187–210 (1985).Google Scholar
  4. 4.
    M. D. Donsker and S. R. S. Varadhan, Asymptotics for the Wiener sausage,Commun. Pure Appl. Math. 28:525–565 (1975).Google Scholar
  5. 5.
    M. D. Donsker and S. R. S. Varadhan, Asymptotics for the polaron,Commun. Pure Appl. Math. 36:505–528 (1983).Google Scholar
  6. 6.
    M. D. Donsker and S. R. S. Varadhan, On laws of the iterated logarithm for local times,Commun. Pure Appl. Math. 30:707–753 (1977).Google Scholar
  7. 7.
    S. R. S. Varadhan, Asymptotic probabilities and differential equations,Commun. Pure Appl. Math. 19:261–286 (1966).Google Scholar
  8. 8.
    T. Y. Lee, Large deviation theory for empirical density of the noninteracting infinite particle systems, Thesis, Courant Institute, New York University (June 1986).Google Scholar
  9. 9.
    J. T. Cox and D. Griffeath, Large deviations for some infinite particle system occupation times,Contemp. Math. 41:43–53 (1985).Google Scholar
  10. 10.
    R. S. Ellis,Entropy, Large Deviations, and Statistical Mechanics (Springer-Verlag, New York, 1985).Google Scholar

Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • M. D. Donsker
    • 1
  • S. R. S. Varadhan
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew York

Personalised recommendations