Zero Range Condensation at Criticality

Abstract

Zero-range processes with decreasing jump rates exhibit a condensation transition, where a positive 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 or subtracting 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 zero to a positive value at a critical scale. Our results also include distributional limits for the fluctuations of the maximum, which change from standard extreme value statistics to Gaussian when the density crosses the critical point. Fluctuations in the bulk are also covered, showing that the mass outside the maximum is distributed homogeneously. In summary, we identify the detailed behaviour at the critical scale including sub-leading terms, which provides a full understanding of the crossover from sub- to supercritical behaviour.

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Cited by in corpus (28)

• Conditional Distribution of Heavy Tailed Random Variables on Large Deviations of their Sum
• Condensation in stochastic particle systems with stationary product measures
• Finite size effects and metastability in zero-range condensation
• Condensation transition in joint large deviations of linear statistics
• Metastability in a condensing zero-range process in the thermodynamic limit
• Condensation for random variables conditioned by the value of their sum
• Coarsening dynamics in condensing zero-range processes and size-biased birth death chains
• Condensation and extremes for a fluctuating number of independent random variables
• Random partitions in statistical mechanics
• Hydrodynamic Limit of mean zero condensing Zero Range Processes with sub-critical initial profiles
• Structure of the condensed phase in the inclusion process
• Derivation of mean-field equations for stochastic particle systems
• Explosive condensation in symmetric mass transport models
• Conditioned random walks and interaction-driven condensation
• A dynamical transition and metastability in a size-dependent zero-range process
• Monotonicity and Condensation in Homogeneous Stochastic Particle Systems
• Condensation and symmetry-breaking in the zero-range process with weak site disorder
• Metastability for a non-reversible dynamics: the evolution of the condensate in totally asymmetric zero range processes
• Critical dynamics of the jamming transition in one-dimensional nonequilibrium lattice-gas models
• Metastable behavior of weakly mixing Markov chains: the case of reversible, critical zero-range processes
• On Random Allocation Models in the Thermodynamic Limit
• A martingale problem for an absorbed diffusion: the nucleation phase of condensing zero range processes
• Poisson-Dirichlet asymptotics in condensing particle systems
• Condensation in models with factorized and pair-factorized stationary states
• Singularity analysis for heavy-tailed random variables
• Collective vs. individual behaviour for sums of i.i.d. random variables: appearance of the one-big-jump phenomenon
• Partition function zeros of zeta-urns
• Generalized Young measures and the hydrodynamic limit of condensing zero range processes