A topical review of ASEP steady-state combinatorics that derives a new determinant form of the TASEP partition function and proposes an unproven bijection between decorated Motzkin paths and permutations.
Stationary distributions of the multi-type ASEP
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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.
fields
cond-mat.stat-mech 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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Combinatorial mappings of exclusion processes
A topical review of ASEP steady-state combinatorics that derives a new determinant form of the TASEP partition function and proposes an unproven bijection between decorated Motzkin paths and permutations.