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Monotonicity and condensation in homogeneous stochastic particle systems
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Rafferty, Thomas, Chleboun, Paul and Grosskinsky, Stefan (2018) Monotonicity and condensation in homogeneous stochastic particle systems. Annales de l'Institut Henri Poincare (B) Probability and Statistics, 54 (2). pp. 790-818. doi:10.1214/17-AIHP821 ISSN 0246-0203.
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Official URL: http://doi.org/10.1214/17-AIHP821
Abstract
We study stochastic particle systems that conserve the particle density and exhibit a condensation transition due to particle interactions. We restrict our analysis to spatially homogeneous systems on fixed finite lattices with stationary product measures, which includes previously studied zero-range or misanthrope processes. All known examples of such condensing processes are non-monotone, i.e. the dynamics do not preserve a partial ordering of the state space and the canonical measures (with a fixed number of particles) are not monotonically ordered. For our main result we prove that condensing homogeneous particle systems with finite critical density are necessarily non-monotone. On fixed finite lattices condensation can occur even when the critical density is infinite, in this case we give an example of a condensing process that numerical evidence suggests is monotone, and give a partial proof of its monotonicity
Item Type: | Journal Article | ||||||||||
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Alternative Title: | |||||||||||
Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||
Library of Congress Subject Headings (LCSH): | Condensation, Stochastic analysis | ||||||||||
Journal or Publication Title: | Annales de l'Institut Henri Poincare (B) Probability and Statistics | ||||||||||
Publisher: | Institute of Mathematical Statistics | ||||||||||
ISSN: | 0246-0203 | ||||||||||
Official Date: | 25 April 2018 | ||||||||||
Dates: |
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Volume: | 54 | ||||||||||
Number: | 2 | ||||||||||
Page Range: | pp. 790-818 | ||||||||||
DOI: | 10.1214/17-AIHP821 | ||||||||||
Status: | Peer Reviewed | ||||||||||
Publication Status: | Published | ||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||
Date of first compliant deposit: | 5 March 2018 | ||||||||||
Date of first compliant Open Access: | 8 May 2018 | ||||||||||
RIOXX Funder/Project Grant: |
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