Skip to main content
SpringerLink
Log in

Large deviations for Glauber dynamics of continuous gas

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

This paper is devoted to the large deviation principles of the Glauber-type dynamics of finite or infinite volume continuous particle systems. We prove that the level-2 empirical process satisfies the large deviation principles in the weak convergence topology, while it does not satisfy the large deviation principles in the τ-topology.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ledoux M. Logarithmic Sobolev inequalities for unbounded spin systems revisited. Séminaire de Probabilités. Lect Notes Math, Vol 1755. New York: Springer, 2001, 167–194

    Google Scholar 

  2. Martinelli F. Lectures on Glauber dynamics for discrete spin models. Ecole d’Eté de Saint-Flour, (1997), Lect Notes in Math, Vol 1717. New York: Springer, 1999, 93–191

    Google Scholar 

  3. Yau H T. Logarithmic Sobolev inequality for lattice gases with mixing conditions. Comm Math Phys, 181: 67–408 (1996)

    Article  Google Scholar 

  4. Preston C. Spatial birth-and-death processes. In: Proceedings of the 40th Session of the International Statistical Institute (Warsaw, 1975), Vol 2; Bull Inst Internat Statist, 46: 371–391 (1975)

    MathSciNet  Google Scholar 

  5. Holley A, Stroock D W. Nearest neighbor birth and death processes on the real line. Acta Math, 140: 103–154 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bertini L, Cancrini N, Cesi F. The spectral gap for a Glauber-type dynamics in a continuous gas. Ann Inst H Poincaré-PR, 38(1): 91–108 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  7. Wu L. Estimate of spectral gap for continuous gas. Ann Inst H Poincaré Probab Stat, 40: 387–409 (2004)

    Article  MATH  Google Scholar 

  8. Kondratiev Y, Lytvynov E. Glauber dynamics of continuous particle systems. Ann Inst H Poincaré-PR, 41: 685–702 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  9. Liu L, Song Q, Wu L. On Glauber dynamics of continous gas. Submitted

  10. Donsker M D, Varadhan S R S. Asymptotic evaluation of certain Markov process expectations for large time, I–IV. Comm Pure Appl Math, 28: 1–47, 279–301 (1975); 29: 389–461 (1976); 36: 183–212 (1983)

    MATH  MathSciNet  Google Scholar 

  11. Deuschel J D, Stroock D W. Large deviations. In: Pure Appl Math, Vol 137. San Diego: Academic Press, 1989

    Google Scholar 

  12. Dembo A, Zeitouni O. Large Deviations Techniques and Applications. New York: Springer, 1998

    MATH  Google Scholar 

  13. Wu L. Uniformly integrable operators and large deviations for Markov processes. J Funct Anal, 172: 301–367 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  14. Wu L. Essential spectral radius for Markor semigroups (I): discrete time case. Probab Theory Related Fields, 128: 255–321 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  15. Wu L. Feynman-Kac semigroups, ground state diffusions and large deviations. J Funct Anal, 123: 202–231 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  16. Ruell D. Statistical Mechanics: Rigorous Results. Singapore: World Scientific, 1969

    Google Scholar 

  17. Malyshev V A, Minlos R A. Gibbs Random Fields: Cluster Expansions. Dordrecht: Kluwer Acad Publ, 1991

    MATH  Google Scholar 

  18. Ma Z, Roeckner M. An Introduction to the Theory of (Non-symmetric) Dirichlet Forms. Berlin: Springer Verlag, 1992

    Google Scholar 

  19. Wu L. Habilitation à diriger des recherches, Laboratiore des probalités. Université Prris VI, 1993

  20. Laurent P L. Approximation et Optimisation. Collection Enseignement des Sciences, Vol 13. Hermann, 1967

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Wuhan University, Wuhan, 430072, China

    QiongXia Song

  2. Department of Statistics and Probability, Michigan State University, East Lansing, MI48824, USA

    QiongXia Song

Authors
  1. QiongXia Song
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to QiongXia Song.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Song, Q. Large deviations for Glauber dynamics of continuous gas. Sci. China Ser. A-Math. 51, 973–986 (2008). https://doi.org/10.1007/s11425-008-0025-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-008-0025-z

Keywords

MSC(2000)

Search

Navigation