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We study the finite zero-range process with occupancy-dependent rate function g • . 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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Let Z . = (Z 1 , Z 2 , . . . , Z n ) represent the steady state of a zero-range process in which n sites are occupied by m particles, with a jump rate between sites given by g. If m = n (a particle density of 1) and Z * n is the maximum cluster size, perfect condensation occurs if n − Z * n converges to 0 in probability as n tends to infinity. In this paper, we improve the description of the conditions for perfect condensation, first introduced by Jeon

No abstract