Zero-range condensation at criticality

Zero-range processes with jump rates that decrease with the number of particles per site can exhibit a condensation transition, where a positive fraction of all particles condenses on a single site when the total density exceeds a critical value. We consider rates which decay as a power law or a stretched exponential to a non-zero limiting value, and study the onset of condensation at the critical density. We establish a law of large numbers for the excess mass fraction in the maximum, as well as distributional limits for the fluctuations of the maximum and the fluctuations in the bulk. (C) 2013 Elsevier B.V. All rights reserved.