Microscopic concavity and fluctuation bounds in a class of deposition processes

Marton Balazs*, Julia Komjathy, Timo Seppalainen

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

19 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)151-187
Number of pages37
JournalAnnales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
Volume48
Issue number1
DOIs
Publication statusPublished - Feb 2012

Keywords

  • Interacting particle systems
  • Universal fluctuation bounds
  • t(1/3)-scaling
  • Second class particle
  • Convexity
  • Asymmetric simple exclusion
  • Zero range process
  • SIMPLE EXCLUSION PROCESS
  • ZERO-RANGE PROCESS
  • ATTRACTIVE PARTICLE-SYSTEMS
  • GROWTH-MODEL
  • POLYNUCLEAR GROWTH
  • CURRENT VARIANCE
  • DIFFUSIVITY
  • SPACE
  • LIMIT
  • ASYMPTOTICS

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