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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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