We consider an infinite system of point particles whose interaction is described by a stable two-body interaction potential ϕ of infinite range. A sequence of finite interaction potentials ϕ R pointwise convergent to ϕ as R → ∞ is introduced. It is shown that the corresponding sequence of correlation functions ρ R converges to ρ in the norm of the Ruelle space E ξ.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. L. Dobrushin, Ya. G. Sinai, and Yu. M. Sukhov, “Dynamic Systems of Statistical Mechanics” (in Russian), in: Itogi VINITI, Ser. Contemporary Problems of Mathematics. Fundamental Directions, Vol. 2, Nauka, Moscow (1985), pp. 235–284.
J. Kerstan, Infinite Divisible Point Processes, J. Kerstan, K. Mattes, and J. Mekke, Nauka, Moscow (1982).
S. Albeverio, Yu. G. Kondratiev, and M. R¨ockner, “Analysis and geometry on configuration spaces,” J. Funct. Anal., 154, No. 2, 444–500 (1998).
D. Ruelle, Statistical Mechanics, Rigorous Results, Benjamin, New York–Amsterdam (1969).
D. Ya. Petrina, V. I. Gerasimenko, and P. V. Malyshev, Mathematical Foundations of Classical Statistical Mechanics, Naukova Dumka, Kiev (1985).
D. Ya. Petrina, V. I. Gerasimenko, and P. V. Malyshev, Mathematical Foundations of Classical Statistical Mechanics, Continuous Systems, Taylor & Francis (2nd Ed.), New-York–London (2002).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 10, pp. 1342–1349, October, 2013.
Rights and permissions
About this article
Cite this article
Malyshev, P.V., Rebenko, A.L. Approximation by Finite Potentials. Ukr Math J 65, 1490–1497 (2014). https://doi.org/10.1007/s11253-014-0874-2
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-014-0874-2