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Zero range condensation at criticality
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Armendáriz, Inés, Grosskinsky, Stefan and Loulakis, Michail. (2013) Zero range condensation at criticality. Stochastic Processes and their Applications, Volume 123 (Number 9). pp. 34663496. ISSN 03044149

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Official URL: http://dx.doi.org/10.1016/j.spa.2013.04.021
Abstract
Zerorange 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 subleading terms, which provides a full understanding of the crossover
from sub to supercritical behaviour.
Item Type:  Journal Article 

Subjects:  Q Science > QC Physics 
Divisions:  Faculty of Science > Mathematics 
Library of Congress Subject Headings (LCSH):  Stochastic systems, Condensation 
Journal or Publication Title:  Stochastic Processes and their Applications 
Publisher:  Elsevier Science BV 
ISSN:  03044149 
Official Date:  September 2013 
Volume:  Volume 123 
Number:  Number 9 
Page Range:  pp. 34663496 
Identification Number:  10.1016/j.spa.2013.04.021 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Restricted or Subscription Access 
References:  [1] E.D. Andjel: Invariant measures for the zero range process. Ann. Probab. 10 (3): 525–547 (1982). 
URI:  http://wrap.warwick.ac.uk/id/eprint/35937 
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