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SIZE OF THE CLUSTERS UNDER LOW DENSITY ZERO-RANGE INVARIANT MEASURES

Jeon, In-Tae

  • Published : 2005.10.01

Abstract

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.[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 ~ $n^{\beta}$,0 < ${\beta}$ < 1, we show that there is an interesting cutoff point around $\beta$ = 1/2.

Keywords

zero-range process;low density;invariant measure;cluster size;cutoff point

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