q-Zero Range has Random Walking Shocks

Marton Balazs*, Lewis Duffy, Dimitri Pantelli

*Corresponding author for this work

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

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Abstract

... but no other surprises in the zero range world. We check all nearest neighbour 1-dimensional asymmetric zero range processes for random walking product shock measures as demonstrated already for a few cases in the literature. We find the totally asymmetric version of the celebrated q-zero range process as the only new example besides an already known model of doubly infinite occupation numbers and exponentially increasing jump rates. We also examine the interaction of shocks, which appears somewhat more involved for q-zero range than in the already known cases.
Original languageEnglish
Pages (from-to)958-971
Number of pages14
JournalJournal of Statistical Physics
Volume174
Issue number5
Early online date6 Jan 2019
DOIs
Publication statusPublished - 10 Mar 2019

Keywords

  • Interacting particle systems
  • second class particle
  • shock measure
  • exact solution
  • q-zero range process

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