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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  
Dates: 


Volume:  Volume 123  
Number:  Number 9  
Page Range:  pp. 34663496  
Identifier:  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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