Zero-range condensation at criticality

Zero-range processes with decreasing jump rates exhibit a continuous condensation transition, where a finite fraction of all particles condenses on a single lattice site when the total density exceeds a critical value. We study the onset of condensation, i.e. the behaviour of the maximum occupation number after adding a subextensive excess mass of particles at the critical density. We establish a law of large numbers for the excess mass fraction in the maximum, which turns out to jump from 0 to a positive value at a critical scale. Our results also include distributional limits for the fluctuations of the maximum in both regimes, which change from standard extreme value statistics to Gaussian. We identify the detailed behaviour at the critical scale including sub-leading terms, providing a full understanding of the crossover between the two regimes.

(Joint work with Ines Armendariz, Michalis Loulakis and Paul Chleboun)

 

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