Journal
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
Volume 48, Issue 1, Pages 151-187Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/11-AIHP415
Keywords
Interacting particle systems; Universal fluctuation bounds; t(1/3)-scaling; Second class particle; Convexity; Asymmetric simple exclusion; Zero range process
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Funding
- Hungarian Scientific Research Fund (OTKA) [K60708, TS49835, F67729]
- Morgan Stanley Mathematical Modeling Center
- Hungarian Academy of Sciences
- National Science Foundation [DMS-07-01091, DMS-10-03651]
- Wisconsin Alumni Research Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1003651] Funding Source: National Science Foundation
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We prove fluctuation bounds for the particle current in totally asymmetric zero range processes in one dimension with nondecreasing, concave jump rates whose slope decays exponentially. Fluctuations in the characteristic directions have order of magnitude t(1/3). This is in agreement with the expectation that these systems lie in the same KPZ universality class as the asymmetric simple exclusion process. The result is via a robust argument formulated for a broad class of deposition-type processes. Besides this class of zero range processes, hypotheses of this argument have also been verified in the authors' earlier papers for the asymmetric simple exclusion and the constant rate zero range processes, and are currently under development for a bricklayers process with exponentially increasing jump rates.
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