Communications in Mathematical Physics

, Volume 78, Issue 4, pp 479–497 | Cite as

Statistical properties of lorentz gas with periodic configuration of scatterers

  • L. A. Bunimovich
  • Ya. G. Sinai
Article

Abstract

In our previous paper Markov partitions for some classes of dispersed billiards were constructed. Using these partitions we estimate the decay of velocity auto-correlation function and prove the central limit theorem of probability theory and Donsker's Invariance Principle for Lorentz Gas with periodic configuration of scatterers.

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References

  1. 1.
    Keller, G.: Diplomarbeit, Erlangen-Nürnberg 1977Google Scholar
  2. 2.
    Bunimovich, L.A., Sinai, Ya.G.: Markov partitions for dispersed billiards. Commun. Math. Phys.77, 247–280 (1980)CrossRefGoogle Scholar
  3. 3.
    Doob, J.L.: Stochastic processes. New York: Wiley and Sons 1950Google Scholar
  4. 4.
    Gnedenko, B.V., Kolmogorov, A.N.: Limit theorems for sums of independent random variables. Moscow: Gostehizdat (1947)Google Scholar
  5. 5.
    Billingsley, P.: Convergence of probability measures. New York: Wiley and Sons 1970Google Scholar
  6. 6.
    Prohorov, Ju.V.: Theory of probabilities and its applications, Vol. 1, No. 2, p. 177 (1956)Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • L. A. Bunimovich
    • 1
  • Ya. G. Sinai
    • 1
  1. 1.Landau Institute of Theoretical PhysicsAcademy of Sciences of the UdSSRMoscowUSSR

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