Stationary distributions of the multi-type ASEP
ELECTRONIC JOURNAL OF PROBABILITY(2020)
摘要
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.
更多查看译文
关键词
asymmetric simple exclusion process,multi-type,matrix product,priority queue
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络