Communications of the
Korean Mathematical Society CKMS

Regarding all particles at a fixed site as a cluster, the size of the largest cluster under the zero range invariant measures is well studied by Jeon et al.\cite{5} for the case of density one. Here, the density of the finite zero-range process is given by the ratio between the number $m$ of particles and the number $n$ of sites. In this paper, we study the lower density case, i.e., the case $m=o(n).$ Especially, when $m\sim n^{\be}, 0<\be

Keywords: zero-range process, low density, invariant measure, cluster size, cutoff point

MSC numbers: 60K35, 82C22