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Stationary distributions of the multi-type ASEP
- Source :
- Electron. J. Probab.
- Publication Year :
- 2018
- Publisher :
- arXiv, 2018.
-
Abstract
- 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 $Z$. 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.<br />Comment: 54 pages, 4 figures
- Subjects :
- Statistics and Probability
multi-type
Pure mathematics
Finite ring
Ring (mathematics)
Stationary distribution
Probability (math.PR)
Rational function
Type (model theory)
asymmetric simple exclusion process
Asymmetric simple exclusion process
Matrix multiplication
Integer
60K35
FOS: Mathematics
matrix product
82C22
Statistics, Probability and Uncertainty
priority queue
Mathematics - Probability
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- Electron. J. Probab.
- Accession number :
- edsair.doi.dedup.....004930b8c47132d0811527bf36a67cf6
- Full Text :
- https://doi.org/10.48550/arxiv.1810.10650