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Condensation and symmetry-breaking in the zero-range process with weak site disorder

Author

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  • Mailler, Cécile
  • Mörters, Peter
  • Ueltschi, Daniel

Abstract

Condensation phenomena in particle systems typically occur as one of two distinct types: either as a spontaneous symmetry breaking in a homogeneous system, in which particle interactions enforce condensation in a randomly located site, or as an explicit symmetry breaking in a system with background disorder, in which particles condensate in the site of extremal disorder. In this paper we confirm a recent conjecture by Godrèche and Luck by showing, for a zero range process with weak site disorder, that there exists a phase where condensation occurs with an intermediate type of symmetry-breaking, in which particles condensate in a site randomly chosen from a range of sites favoured by disorder. We show that this type of condensation is characterised by the occurrence of a Gamma distribution in the law of the disorder at the condensation site. We further investigate fluctuations of the condensate size and confirm a phase diagram, again conjectured by Godrèche and Luck, showing the existence of phases with normal and anomalous fluctuations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:11:p:3283-3309
    DOI: 10.1016/j.spa.2016.04.028
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    References listed on IDEAS

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    1. Armendáriz, Inés & Grosskinsky, Stefan & Loulakis, Michail, 2013. "Zero-range condensation at criticality," Stochastic Processes and their Applications, Elsevier, vol. 123(9), pages 3466-3496.
    2. 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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