The TAZRP speed process

Journal article

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.

Authors: Amir, G; Busani, O; Gonçalves, P; Martin, J

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Institute of Mathematical Statistics
• Journal: Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
• Volume: 57
• Issue: 3
• Pages: 1281–1305
• Publication date: 2021-07-22
• Acceptance date: 2020-10-22
• DOI: 10.1214/20-AIHP1117
• ISSN: 0246-0203
• Language: English
• Keywords: speed of a second class particle; zero range process; FFR; speed process