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Convergence to a stationary state and diffusion for a charged particle in a standing medium
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  • Published: February 1989

Convergence to a stationary state and diffusion for a charged particle in a standing medium

  • C. Boldrighini1,
  • G. C. Cosimi1,
  • S. Frigio1 &
  • …
  • A. Nogueira2 

Probability Theory and Related Fields volume 80, pages 481–500 (1989)Cite this article

  • 57 Accesses

  • 5 Citations

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Summary

We study a one-dimensional semi-infinite system of identical particles, driven by a constant force acting only on the first particle. Particles interact through elastic collisions. At time zero all particles are at rest, and the interparticle distances are i.i.d. r.v.'s, the support of the distribution being in (d, ∞), d>0. We show that if d is large enough the dynamics has a strong cluster property, and prove, for large times, convergence to a limiting distribution for the system as seen from the first particle, as well as existence of drift velocity and invariance principle for the motion of the first particle.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Fisica, Università di Camerino, I-62032, Camerino, Italy

    C. Boldrighini, G. C. Cosimi & S. Frigio

  2. Instituto de Matemática, Universidade Federal do Rio de Janeiro, University of Rio de Janeiro, 21944, Rio de Janeiro, RJ, Brazil

    A. Nogueira

Authors
  1. C. Boldrighini
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  2. G. C. Cosimi
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  3. S. Frigio
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  4. A. Nogueira
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Additional information

Partially supported by C.N.R.-C.N.Pq. agreement

Partially supported by M.P.I. research funds

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Boldrighini, C., Cosimi, G.C., Frigio, S. et al. Convergence to a stationary state and diffusion for a charged particle in a standing medium. Probab. Th. Rel. Fields 80, 481–500 (1989). https://doi.org/10.1007/BF00318904

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  • Received: 20 December 1986

  • Revised: 06 June 1988

  • Issue Date: February 1989

  • DOI: https://doi.org/10.1007/BF00318904

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Keywords

  • Stochastic Process
  • Stationary State
  • Charged Particle
  • Probability Theory
  • Statistical Theory
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