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Brownian asymptotics in a Poissonian environment
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  • Published: June 1993

Brownian asymptotics in a Poissonian environment

  • Alain-Sol Sznitman1 

Probability Theory and Related Fields volume 95, pages 155–174 (1993)Cite this article

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Summary

We consider a Brownian motion moving in a random potential obtained by translating a given fixed non negative shape function at the points of a Poisson cloud. We derive the almost sure principal long time behavior of the expectation of the natural Feynman Kac functional, which is insensitive to the detail of the shape function. We also study the situation of hard obstacles where Brownian motion is killed once it comes within distancea of a point of the cloud. The nature of the results then changes between the case whena is small or large in connection with the presence, or absence of an infinite component in the complement of the obstacles.

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Authors and Affiliations

  1. Departement Mathematik, ETH-Zentrum, CH-8092, Zürich, Switzerland

    Alain-Sol Sznitman

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  1. Alain-Sol Sznitman
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Cite this article

Sznitman, AS. Brownian asymptotics in a Poissonian environment. Probab. Th. Rel. Fields 95, 155–174 (1993). https://doi.org/10.1007/BF01192268

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  • Received: 01 August 1991

  • Revised: 23 June 1992

  • Issue Date: June 1993

  • DOI: https://doi.org/10.1007/BF01192268

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Mathematics Subject Classification (1991)

  • 60 K 40
  • 82 D 30
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