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