The TAZRP speed process

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

doi:10.1214/20-aihp1117

The TAZRP speed process

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

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	1281-1305
Number of pages	25
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	57
Issue number	3
DOIs	https://doi.org/10.1214/20-aihp1117
State	Published - Aug 2021

Keywords

Speed of a second class particle
Speed process
Zero range process

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/20-aihp1117

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title = "The TAZRP speed process",

abstract = "In (Ann. Probab. 39 (4) (2011) 1205–1242) Amir, Angel and Valk{\'o} 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.",

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month = aug,

doi = "10.1214/20-aihp1117",

language = "الإنجليزيّة",

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AU - Amir, Gideon

AU - Busani, Ofer

AU - Gonçalves, Patrícia

AU - Martin, James B.

N1 - Publisher Copyright: © Association des Publications de l’Institut Henri Poincaré, 2021.

PY - 2021/8

Y1 - 2021/8

N2 - 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.

AB - 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.

KW - Speed of a second class particle

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DO - 10.1214/20-aihp1117

M3 - مقالة

SN - 0246-0203

VL - 57

SP - 1281

EP - 1305

JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

IS - 3

ER -

The TAZRP speed process

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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