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

Title & Authors
SIZE OF THE CLUSTERS UNDER LOW DENSITY ZERO-RANGE INVARIANT MEASURES
Jeon, In-Tae;

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 ~ $\small{n^{\beta}}$,0 < $\small{{\beta}}$ < 1, we show that there is an interesting cutoff point around $\small{\beta}$ = 1/2.
Keywords
zero-range process;low density;invariant measure;cluster size;cutoff point;
Language
English
Cited by
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