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A tagged particle process in the Boltzmann-Grad limit for the Broadwell modell
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  • Published: August 1989

A tagged particle process in the Boltzmann-Grad limit for the Broadwell modell

  • Kôhei Uchiyama1 

Probability Theory and Related Fields volume 82, pages 419–433 (1989)Cite this article

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  • 2 Citations

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Summary

We study a tagged particle process for a model dynamical system in which identical particles move deterministically with discrete velocities, initially starting from a random configuration. We pass to the Boltzmann-Grad limit so that the tagged particle process converges to a nontrivial process (for short times). We can show that recollisions are vanishing in this limit, and this fact may have one expect that the limiting process would be Markovian. Nevertheless it is not Markovian, for which claim we give intuitive reasoning as well as a mathematical proof.

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References

  1. Spohn, H.: Kinetic equations from Hamiltonian dynamics: Markov limits. Rev. Mod. Phys. 53, 569 (1980)

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  2. Uchiyama, K.: On the Boltzmann-Grad limit for the Broadwell model of the Boltzmann equation. J. Stat. Phys. 52, 331–355 (1988)

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  3. Uchiyama, K.: Derivation of the Boltzmann equation from particle dynamics. Hiroshima Math. J. 18, 245–297 (1988)

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Author information

Authors and Affiliations

  1. Department of Mathematics, Hiroshima University, Higashi Senda-machi, 730, Hiroshima, Japan

    Kôhei Uchiyama

Authors
  1. Kôhei Uchiyama
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Additional information

Supported in part by Grant-in-Aid for Scientific Research (No. 62302006), Ministry of Education, Science and Culture

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Cite this article

Uchiyama, K. A tagged particle process in the Boltzmann-Grad limit for the Broadwell modell. Probab. Th. Rel. Fields 82, 419–433 (1989). https://doi.org/10.1007/BF00339996

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  • Received: 16 May 1988

  • Revised: 24 February 1989

  • Issue Date: August 1989

  • DOI: https://doi.org/10.1007/BF00339996

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Keywords

  • Dynamical System
  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Mathematical Proof
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