Finite size effects and metastability in zero-range condensation

Abstract

We study zero-range processes which are known to exhibit a condensation transition, where above a critical density a non-zero fraction of all particles accumulates on a single lattice site. This phenomenon has been a subject of recent research interest and is well understood in the thermodynamic limit. The system shows large finite size effects, and we observe a switching between metastable fluid and condensed phases close to the critical point, in contrast to the continuous limiting behaviour of relevant observables. We describe the leading order finite size effects and establish a discontinuity near criticality in a rigorous scaling limit. We also characterise the metastable phases using a current matching argument and an extension of the fluid phase to supercritical densities. This constitutes an interesting example where the thermodynamic limit fails to capture essential parts of the dynamics, which are particularly relevant in applications with moderate system sizes such as traffic flow or granular clustering.

30 pages, 8 figures; typos corrected, figures improved, added references

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Cited by in corpus (28)

• Diffusions conditioned on occupation measures
• Condensation in stochastic particle systems with stationary product measures
• Zero Range Condensation at Criticality
• Inequivalence of nonequilibrium path ensembles: the example of stochastic bridges
• Condensation transition in joint large deviations of linear statistics
• Metastability in a condensing zero-range process in the thermodynamic limit
• The grand canonical catastrophe as an instance of condensation of fluctuations
• Large deviations, condensation, and giant response in a statistical system
• Condensation for random variables conditioned by the value of their sum
• Development and regression of a large fluctuation
• Coarsening dynamics in condensing zero-range processes and size-biased birth death chains
• Structure of the condensed phase in the inclusion process
• Probability distributions with singularities
• Explosive condensation in symmetric mass transport models
• Two-point correlation function of an exclusion process with hole-dependent rates
• A dynamical transition and metastability in a size-dependent zero-range process
• Lower current large deviations for zero-range processes on a ring
• Monotonicity and Condensation in Homogeneous Stochastic Particle Systems
• Condensation and symmetry-breaking in the zero-range process with weak site disorder
• On Random Allocation Models in the Thermodynamic Limit
• Condensation in randomly perturbed zero-range processes
• Dynamics of fluctuations in the Gaussian model with conserved dynamics
• Finite-size effects in dynamics of zero-range processes
• Partition function zeros of zeta-urns
• Emergence of dynamic phases in the presence of different kinds of open boundaries in stochastic transport with short-range interactions
• Dynamics of condensate formation in stochastic transport with pair-factorized steady states: Nucleation and coarsening time scales
• Dynamics of fluctuations in the Gaussian model with dissipative Langevin Dynamics
• Condensation in zero-range processes with a fast rate