Skip to main content
SpringerLink
Log in

Estimate of convergence rate in local limit theorem for the particle number in spin systems

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

For classical lattice spin systems with vacuum, an estimate is obtained of the convergence rate in a local limit theorem for the number of particles in a region A. The estimate has the order of the square rooot of the volume of A.

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. V. A. Arzumanyan, B. S. Nakhapetyan, and S. K. Pogosyan,Teor. Mat. Fiz.,67, 21 (1986).

    Google Scholar 

  2. V. A. Arzumanyan, B. S. Nakhapetyan, and S. K. Pogosyan,Teor. Mat. Fiz.,81, 175 (1989).

    Google Scholar 

  3. V. A. Arzumanyan, B. S. Nakhapetyan, and S. K. Pogosyan,Teor. Mat. Fiz.,89, 178 (1991).

    Google Scholar 

  4. V. A. Arzumanian, B. S. Nahapetian, S. K. Pogosian,Acta Applicandae Mathematicae,22, 33 (1991).

    Google Scholar 

  5. S. K. Pogosian,Random Fields, Rigorous Results in Statistical Mechanics and Quantum Field Theory, Estergom, Hungary (1979), p. 889.

  6. S. K. Pogosian,Commun. Math. Phys.,95, 227 (1984).

    Google Scholar 

  7. D. Ruelle,Statistical Mechanics, New York (1969).

  8. R. L. Dobrushin,Teor. Veroyatn. Ee Primen.,2, 201 (1968).

    Google Scholar 

  9. R. L. Dobrushin,Funktsional Analiz i Ego Prilozhen.,4, 31 (1968).

    Google Scholar 

  10. B. S. Nahapetian,Limit Theorems and Some Applications in Statistical Physics, Teubner-Texte zur Mathematik, Stuttgart-Leipzig (1991).

    Google Scholar 

  11. I. A. Ibragimov and Yu. V. Linnik,Independent and Steadily Coupled Variables [in Russian], Nauka, Moscow (1965).

    Google Scholar 

  12. R. L. Dobrushin and B. S. Nakhapetyan,Teor. Mat. Fiz.,20, 223 (1974).

    Google Scholar 

Download references

Authors
  1. B. S. Nakhapetyan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. K. Pogosyan
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Institute of Mathematics, Armenian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 3, pp. 497–512, June, 1993.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nakhapetyan, B.S., Pogosyan, S.K. Estimate of convergence rate in local limit theorem for the particle number in spin systems. Theor Math Phys 95, 738–747 (1993). https://doi.org/10.1007/BF01017519

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01017519

Keywords

Search

Navigation