The Annals of Probability

Size of the largest cluster under zero-range invariant measures

Intae Jeon, Peter March, and Boris Pittel

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Abstract

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.

Article information

Source
Ann. Probab., Volume 28, Number 3 (2000), 1162-1194.

Dates
First available in Project Euclid: 18 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1019160330

Digital Object Identifier
doi:10.1214/aop/1019160330

Mathematical Reviews number (MathSciNet)
MR1797308

Zentralblatt MATH identifier
1023.60084

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C22: Interacting particle systems [See also 60K35]

Keywords
Zero-range process equilibrium measure cluster size random partition local limit theorem

Citation

Jeon, Intae; March, Peter; Pittel, Boris. Size of the largest cluster under zero-range invariant measures. Ann. Probab. 28 (2000), no. 3, 1162--1194. doi:10.1214/aop/1019160330. https://projecteuclid.org/euclid.aop/1019160330


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