Random Walk of Second Class Particles in Product Shock Measures

Marton Balazs*, Gyoergy Farkas, Peter Kovacs, Attila Rakos

*Corresponding author for this work

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

16 Citations (Scopus)

Abstract

We consider shock measures in a class of conserving stochastic particle systems on a"currency sign. These shock measures have a product structure with a step-like density profile and include a second class particle at the shock position. We show for the asymmetric simple exclusion process, for the exponential bricklayers' process, and for a generalized zero range process, that under certain conditions these shocks, and therefore the second class particles, perform a simple random walk. Some previous results, including random walks of product shock measures and stationary shock measures seen from a second class particle, are direct consequences of our more general theorem. Multiple shocks can also be handled easily in this framework. Similar shock structure is also found in a nonconserving model, the branching coalescing random walk, where the role of the second class particle is played by the rightmost (or leftmost) particle.

Original languageEnglish
Pages (from-to)252-279
Number of pages28
JournalJournal of Statistical Physics
Volume139
Issue number2
DOIs
Publication statusPublished - Apr 2010

Keywords

  • Interacting particle systems
  • Second class particle
  • Shock measure
  • Exact solution
  • Asymmetric simple exclusion
  • Zero range process
  • Bricklayers process
  • Branching coalescing random walks
  • ZERO-RANGE PROCESS
  • SIMPLE EXCLUSION PROCESS
  • MULTIPLE SHOCKS
  • MODEL
  • SYSTEMS
  • FLUCTUATIONS
  • STATES

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