Journal of Statistical Physics

, Volume 43, Issue 1–2, pp 321–341 | Cite as

On the diffusion of a fast molecule

  • S. Goldstein
  • J. Guetti


We consider the motion of a heavy particle in interaction with an infinite ideal gas of slow atoms. We prove that the velocity of the heavy particle is, in a suitable limit, modeled by a deterministic process. We also treat the process of rescaled velocity fluctuations around a certain deterministic motion and show that this is appropriately modeled by a nonhomogeneous diffusion process.

Key words

Nonhomogeneous diffusion velocity fluctuations Rayleigh piston Markov approximation deterministic limit fluctuations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P. Billingsley,Convergence of Probability Measures (Wiley, New York, 1968).Google Scholar
  2. 2.
    D. Dürr, S. Goldstein, and J. L. Lebowitz,Comm. Math. Phys. 78:507–530 (1981).Google Scholar
  3. 3.
    E. B. Dynkin,Markov Processes I, II (Springer, Berlin, 1965).Google Scholar
  4. 4.
    R. Holley,Z. Wahrsch. Verw. Gebiete 17:181–219 (1971).Google Scholar
  5. 5.
    T. Kurz,Ann. Probability 4:618–642 (1975).Google Scholar
  6. 6.
    B. Miller and W. Stein,J. Stat. Phys. 26(3):539–553 (1981).Google Scholar
  7. 7.
    N. G. Van Kampen,Stochastic Processes in Physics and Chemistry, (North-Holland, Amsterdam, 1981).Google Scholar
  8. 8.
    L. N. Vaserstein,Comm. Math. Phys. 69:31–56 (1979).Google Scholar

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • S. Goldstein
    • 1
  • J. Guetti
    • 2
  1. 1.Department of MathematicsRutgers UniversityNew Brunswick
  2. 2.Department of MathematicsSeton Hall UniversitySouth Orange

Personalised recommendations