Order of current variance and diffusivity in the rate one totally asymmetric zero range process

Márton Balázs, Júlia Komjáthy*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

7 Citations (Scopus)

Abstract

We prove that the variance of the current across a characteristic is of order t 2/3 in a stationary constant rate totally asymmetric zero range process, and that the diffusivity has order t 1/3. This is a step towards proving universality of this scaling behavior in the class of one-dimensional interacting systems with one conserved quantity and concave hydrodynamic flux. The proof proceeds via couplings to show the corresponding moment bounds for a second class particle. We build on the methods developed in Balázs and Seppäläinen (Order of current variance and diffusivity in the asymmetric simple exclusion process, 2006) for simple exclusion. However, some modifications were needed to handle the larger state space. Our results translate into t 2/3-order of variance of the tagged particle on the characteristics of totally asymmetric simple exclusion.

Original languageEnglish
Pages (from-to)59-78
Number of pages20
JournalJournal of Statistical Physics
Volume133
Issue number1
DOIs
Publication statusPublished - Oct 2008

Keywords

  • Constant rate totally asymmetric zero range process
  • Current fluctuations
  • Diffusivity
  • Second class particle

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