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November 2005 Long-range exclusion processes, generator and invariant measures
Enrique D. Andjel, Hervé Guiol
Ann. Probab. 33(6): 2314-2354 (November 2005). DOI: 10.1214/009117905000000486

Abstract

We show that if μ is an invariant measure for the long range exclusion process putting no mass on the full configuration, L is the formal generator of that process and f is a cylinder function, then LfL1() and ∫Lf=0. This result is then applied to determine (i) the set of invariant and translation-invariant measures of the long range exclusion process on ℤd when the underlying random walk is irreducible; (ii) the set of invariant measures of the long range exclusion process on ℤ when the underlying random walk is irreducible and either has zero mean or allows jumps only to the nearest-neighbors.

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Enrique D. Andjel. Hervé Guiol. "Long-range exclusion processes, generator and invariant measures." Ann. Probab. 33 (6) 2314 - 2354, November 2005. https://doi.org/10.1214/009117905000000486

Information

Published: November 2005
First available in Project Euclid: 7 December 2005

zbMATH: 1099.60064
MathSciNet: MR2184098
Digital Object Identifier: 10.1214/009117905000000486

Subjects:
Primary: 60K35

Keywords: ergodic theorems , Invariant measures , Long range exclusion process , non-Feller process

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 6 • November 2005
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