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July 2000 Size of the largest cluster under zero-range invariant measures
Intae Jeon, Peter March, Boris Pittel
Ann. Probab. 28(3): 1162-1194 (July 2000). DOI: 10.1214/aop/1019160330


We study the .nite zero-range process with occupancy-dependent rate function $g(\cdot)$. Under the invariant measure, which can be written explicitly in terms of $g$, particles are distributed over sites and we regard all particles at a fixed site as a cluster. In the density one case, that is, equal numbers of particles and sites, we determine asymptotically the size of the largest cluster, as the number of particles tends to infinity, and determine its dependence on the rate function.


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Intae Jeon. Peter March. Boris Pittel. "Size of the largest cluster under zero-range invariant measures." Ann. Probab. 28 (3) 1162 - 1194, July 2000.


Published: July 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1023.60084
MathSciNet: MR1797308
Digital Object Identifier: 10.1214/aop/1019160330

Primary: 60K35
Secondary: 82C22

Keywords: cluster size , Equilibrium measure , local limit theorem , random partition , Zero-range process

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.28 • No. 3 • July 2000
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