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Some results for long-range exclusion processes
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  • Published: 18 September 2007

Some results for long-range exclusion processes

  • Enrique Andjel1 &
  • T. S. Mountford2 

Probability Theory and Related Fields volume 142, pages 189–217 (2008)Cite this article

  • 81 Accesses

  • 1 Citations

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Abstract

We examine the long-range exclusion process introduced by Spitzer and studied by Liggett and answer some of the open questions raised by Liggett. In particular, we show the existence of equilibria corresponding to bounded dual harmonic functions and that the process can have right-discontinuous paths at strictly positive times. We also show that “explosions” when they occur, do so at fixed times determined by the initial configuration. Finally, we give an example for which the configuration with all sites occupied is not stable although the rate at which particles arrive at any given site for that configuration is infinite.

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Author information

Authors and Affiliations

  1. CMI, Université de Provence, 13453, Marseille cedex 13, France

    Enrique Andjel

  2. Département de Mathématiques, Ecole Polytechnique Fédérale, 1015, Lausanne, Switzerland

    T. S. Mountford

Authors
  1. Enrique Andjel
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  2. T. S. Mountford
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Corresponding author

Correspondence to Enrique Andjel.

Additional information

The research of E. Andjel was partially supported by the European Science Foundations programme: Phase Transitions and Fluctuation Phenomena.

The research of T. S. Mountford is partially supported by the SNF, grant # 200020-115964.

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Cite this article

Andjel, E., Mountford, T.S. Some results for long-range exclusion processes. Probab. Theory Relat. Fields 142, 189–217 (2008). https://doi.org/10.1007/s00440-007-0102-1

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  • Received: 12 May 2005

  • Revised: 26 July 2007

  • Published: 18 September 2007

  • Issue Date: September 2008

  • DOI: https://doi.org/10.1007/s00440-007-0102-1

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Keywords

  • Particle system
  • Coupling

Mathematics Subject Classification (2000)

  • Primary: 60K35
  • Secondary: 82C22
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