Skip to main content
SpringerLink
Log in

The local central limit theorem for a Gibbs random field

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We extend the validity of the implication of a local limit theorem from an integral one. Our extension eliminates the finite range assumption present in the previous works by using the cluster expansion to analyze the contribution from the tail of the potential.

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. Gnedenko, B. V.: The theory of probability. Moscow, Nauka 1965, Engl. Trans. MIR 1976.

    Google Scholar 

  2. Dobrushin, R. L., Tirozzi, B.: Comm. Math. Phys.54, 173–192 (1977)

    Article  Google Scholar 

  3. Campanino, M., Del Grosso, G., Tirozzi, B.: to appear in J. Math. Phys.

  4. Ruelle, D.: Statistical mechanics. New York: Benjamin 1969

    Google Scholar 

  5. Gallavotti, G., Martin-Lof, A., Miracle-Sole, A.: Lecture Notes in Phys.20, 162–202 (1971)

    Google Scholar 

  6. Kunz, H.: Comm. Math. Phys.59, 53 (1978)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto di Matematica “G. Castelnuovo”, University of Rome, Italy

    M. Campanino, D. Capocaccia & B. Tirozzi

  2. Instituto di Matematica, University of Aquila, Italy

    M. Campanino, D. Capocaccia & B. Tirozzi

Authors
  1. M. Campanino
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Capocaccia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. Tirozzi
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by E. Lieb

Rights and permissions

Reprints and permissions

About this article

Cite this article

Campanino, M., Capocaccia, D. & Tirozzi, B. The local central limit theorem for a Gibbs random field. Commun.Math. Phys. 70, 125–132 (1979). https://doi.org/10.1007/BF01982350

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01982350

Keywords

Search

Navigation