Stationary distributions of the multi-type ASEP
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 th...
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| Format: | Journal article |
| Language: | English |
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Institute of Mathematical Statistics and the Bernoulli Society
2020
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| Summary: | 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 qk 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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