Journal of Statistical Physics

, Volume 55, Issue 3–4, pp 787–855 | Cite as

An invariance principle for reversible Markov processes. Applications to random motions in random environments

  • A. De Masi
  • P. A. Ferrari
  • S. Goldstein
  • W. D. Wick


We present an invariance principle for antisymmetric functions of a reversible Markov process which immediately implies convergence to Brownian motion for a wide class of random motions in random environments. We apply it to establish convergence to Brownian motion (i) for a walker moving in the infinite cluster of the two-dimensional bond percolation model, (ii) for ad-dimensional walker moving in a symmetric random environment under very mild assumptions on the distribution of the environment, (iii) for a tagged particle in ad-dimensional symmetric lattice gas which allows interchanges, (iv) for a tagged particle in ad-dimensional system of interacting Brownian particles. Our formulation also leads naturally to bounds on the diffusion constant.

Key words

Symmetric random environment random potential reversible Markov process central limit theorem invariance principle interacting Brownian particles 


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Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • A. De Masi
    • 1
  • P. A. Ferrari
    • 2
  • S. Goldstein
    • 3
  • W. D. Wick
    • 4
  1. 1.Dipartmento di Matematica Pura e ApplicataUniversità dell'AquilaL'AquilaItaly
  2. 2.Instituto de Matemàtica e EstatisticaUniversidade de São PauloSão PauloBrazil
  3. 3.Department of MathematicsRutgers UniversityNew Brunswick
  4. 4.Department of MathematicsUniversity of ColoradoBoulder

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