The TAZRP speed process

Gideon Amir, Ofer Busani, Patrícia Gonçalves, James B. Martin

Research output: Contribution to journalArticlepeer-review


In (Ann. Probab. 39 (4) (2011) 1205–1242) Amir, Angel and Valkó studied a multi-type version of the totally asymmetric simple exclusion process (TASEP) and introduced the TASEP speed process, which allowed them to answer delicate questions about the joint distribution of the speed of several second-class particles in the TASEP rarefaction fan. In this paper we introduce the analogue of the TASEP speed process for the totally asymmetric zero-range process (TAZRP), and use it to obtain new results on the joint distribution of the speed of several second-class particles in the TAZRP with a reservoir. These is a close link from the speed process to questions about stationary distributions of multi-type versions of the TAZRP; for example we are able to give a precise description of the contents of a single site in equilibrium for a multi-type TAZRP with continuous labels.

Original languageEnglish
Pages (from-to)1281-1305
Number of pages25
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Issue number3
StatePublished - Aug 2021

Bibliographical note

Funding Information:
G. Amir was supported by the Israel Science Foundation through grant 575/16 and by the German Israeli Foundation through grant I-1363-304.6/2016. O. Busani was supported by EPSRC’s EP/R021449/1 Standard Grant. P. Gonçalves thanks FCT/Portugal for support through the project UID/MAT/04459/2013. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 715734).

Publisher Copyright:
© Association des Publications de l’Institut Henri Poincaré, 2021.


  • Speed of a second class particle
  • Speed process
  • Zero range process


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