an:04153655
Zbl 0703.60101
Saada, Ellen
Processus de zero-range avec particule marqu??e. (Zero-range process with a tagged particle)
FR
Ann. Inst. Henri Poincar??, Probab. Stat. 26, No. 1, 5-17 (1990).
00155513
1990
j
60K35 60F05
zero-range process; invariant geometric product measure; strong law of large numbers; central limit theorem
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.