Lower Current Large Deviations for Zero-Range Processes on a Ring

Paul Chleboun, Stefan Grosskinsky, Andrea Pizzoferrato

Research output: Contribution to journalArticlepeer-review

Abstract

We study lower large deviations for the current of totally asymmetric zero-range processes on a ring with concave current-density relation. We use an approach by Jensen and Varadhan which has previously been applied to exclusion processes, to realize current fluctuations by travelling wave density profiles corresponding to non-entropic weak solutions of the hyperbolic scaling limit of the process. We further establish a dynamic transition, where large deviations of the current below a certain value are no longer typically attained by non-entropic weak solutions, but by condensed profiles, where a non-zero fraction of all the particles accumulates on a single fixed lattice site. This leads to a general characterization of the rate function, which is illustrated by providing detailed results for four generic examples of jump rates, including constant rates, decreasing rates, unbounded sublinear rates and asymptotically linear rates. Our results on the dynamic transition are supported by numerical simulations using a cloning algorithm.

Original languageEnglish
Pages (from-to)64-89
Number of pages26
JournalJournal of Statistical Physics
Volume167
Issue number1
Early online date13 Feb 2017
DOIs
Publication statusPublished - 30 Apr 2017

Keywords

  • Condensation
  • Current fluctuations
  • Large deviations
  • Zero-range process

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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