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Zero-range condensation at criticality

Author

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  • Armendáriz, Inés
  • Grosskinsky, Stefan
  • Loulakis, Michail

Abstract

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.

Suggested Citation

  • Armendáriz, Inés & Grosskinsky, Stefan & Loulakis, Michail, 2013. "Zero-range condensation at criticality," Stochastic Processes and their Applications, Elsevier, vol. 123(9), pages 3466-3496.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:9:p:3466-3496
    DOI: 10.1016/j.spa.2013.04.021
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    References listed on IDEAS

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    1. Armendáriz, Inés & Loulakis, Michail, 2011. "Conditional distribution of heavy tailed random variables on large deviations of their sum," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 1138-1147, May.
    2. Großkinsky, Stefan, 2008. "Equivalence of ensembles for two-species zero-range invariant measures," Stochastic Processes and their Applications, Elsevier, vol. 118(8), pages 1322-1350, August.
    3. Andjel, E. D. & Ferrari, P. A. & Guiol, H. & Landim *, C., 2000. "Convergence to the maximal invariant measure for a zero-range process with random rates," Stochastic Processes and their Applications, Elsevier, vol. 90(1), pages 67-81, November.
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    Cited by:

    1. Mailler, Cécile & Mörters, Peter & Ueltschi, Daniel, 2016. "Condensation and symmetry-breaking in the zero-range process with weak site disorder," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3283-3309.
    2. Grosskinsky, Stefan & Jatuviriyapornchai, Watthanan, 2019. "Derivation of mean-field equations for stochastic particle systems," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1455-1475.
    3. Landim, C., 2023. "Metastability from the large deviations point of view: A Γ-expansion of the level two large deviations rate functional of non-reversible finite-state Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 165(C), pages 275-315.
    4. Nicholas M. Ercolani & Sabine Jansen & Daniel Ueltschi, 2019. "Singularity Analysis for Heavy-Tailed Random Variables," Journal of Theoretical Probability, Springer, vol. 32(1), pages 1-46, March.

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