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A limit theorem for the position of a tagged particle in a simple exclusion process. (English) Zbl 0617.60096
The author proves a strong law of large numbers for the position of a tagged particle in a stationary simple exclusion process, which verifies a conjecture of T. M. Liggett [Interacting particle systems. (1985; Zbl 0559.60078)].
For this purpose, the process relative to the tagged particle is studied. It is shown, that the Bernoulli measures conditioned on the existence of a particle at the origin, are extremal invariant for this process.
Reviewer: M.Mürmann

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F15 Strong limit theorems
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