Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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SIZE OF THE CLUSTERS UNDER LOW DENSITY ZERO-RANGE INVARIANT MEASURES

  • Jeon, In-Tae (Department of Mathematics The Catholic University of Korea)
  • Published : 2005.10.01
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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.

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References

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