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Long-range exclusion processes, generator and invariant measures - Archive ouverte HAL
Article Dans Une Revue Annals of Probability Année : 2005

Long-range exclusion processes, generator and invariant measures

Hervé Guiol
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Résumé

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(dμ) and Lfdμ=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.

Dates et versions

hal-00273600 , version 1 (15-04-2008)

Identifiants

Citer

Enrique D. Andjel, Hervé Guiol. Long-range exclusion processes, generator and invariant measures. Annals of Probability, 2005, 33 (6), pp.2314-2354. ⟨hal-00273600⟩
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