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

Cecile Mailler, Peter Morters, Daniel Ueltschi

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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 Godreche 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 Godreche and Luck, showing the existence of phases with normal and anomalous fluctuations.
Original languageEnglish
Pages (from-to)3283-3309
Number of pages22
JournalStochastic Processes and their Applications
Issue number11
Early online date6 May 2016
Publication statusPublished - 1 Nov 2016


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