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2020 Stationary distributions of the multi-type ASEP
James B. Martin
Electron. J. Probab. 25: 1-41 (2020). DOI: 10.1214/20-EJP421


We give a recursive construction of the stationary distribution of multi-type asymmetric simple exclusion processes on a finite ring or on the infinite line $\mathbb{Z} $. The construction can be interpreted in terms of “multi-line diagrams” or systems of queues in tandem. Let $q$ be the asymmetry parameter of the system. The queueing construction generalises the one previously known for the totally asymmetric ($q=0$) case, by introducing queues in which each potential service is unused with probability $q^{k}$ when the queue-length is $k$. The analysis is based on the matrix product representation of Prolhac, Evans and Mallick. Consequences of the construction include: a simple method for sampling exactly from the stationary distribution for the system on a ring; results on common denominators of the stationary probabilities, expressed as rational functions of $q$ with non-negative integer coefficients; and probabilistic descriptions of “convoy formation” phenomena in large systems.


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James B. Martin. "Stationary distributions of the multi-type ASEP." Electron. J. Probab. 25 1 - 41, 2020.


Received: 9 November 2018; Accepted: 25 January 2020; Published: 2020
First available in Project Euclid: 3 April 2020

zbMATH: 1441.60083
MathSciNet: MR4089793
Digital Object Identifier: 10.1214/20-EJP421

Primary: 60K35
Secondary: 82C22


Vol.25 • 2020
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