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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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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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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DOI: https://doi.org/10.1007/s00440-007-0102-1
Keywords
- Particle system
- Coupling
Mathematics Subject Classification (2000)
- Primary: 60K35
- Secondary: 82C22