The Library
Zero range condensation at criticality
Tools
Armendáriz, Inés, Grosskinsky, Stefan and Loulakis, Michail (2013) Zero range condensation at criticality. Stochastic Processes and their Applications, Volume 123 (Number 9). pp. 3466-3496. doi:10.1016/j.spa.2013.04.021 ISSN 0304-4149.
|
Text
1070268-lb-060711-wrap_grosskinsky_zero_range_condensation.pdf - Submitted Version Download (327Kb) |
Official URL: http://dx.doi.org/10.1016/j.spa.2013.04.021
Abstract
Zero-range 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 sub-leading 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, Engineering and Medicine > 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: | 0304-4149 | ||||
Official Date: | September 2013 | ||||
Dates: |
|
||||
Volume: | Volume 123 | ||||
Number: | Number 9 | ||||
Page Range: | pp. 3466-3496 | ||||
DOI: | 10.1016/j.spa.2013.04.021 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year