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Processus de zero-range avec particule marquée. (Zero-range process with a tagged particle). (French) Zbl 0703.60101
Summary: We study a zero-range process [for which g(k)\(\equiv 1\) if \(k>0]\) in equilibrium, having as initial distribution the invariant geometric product measure \(\mu_{\rho}\) (0\(\leq \rho \leq 1)\). We prove that the \(\mu_{\rho}\) are extremal invariant in the transient case. We then prove in the symmetric case a strong law of large numbers and a central limit theorem for the position of a “supplementary” (i.e. second class) particle, and also the asymptotic independence of a finite number of second class particles. Finally for the position of a tagged particle we prove a strong law of large numbers and, in the symmetric case, a central limit theorem.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F05 Central limit and other weak theorems
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