Twisted multiline queues for the steady states of TASEP and TAZRP

TL;DR

This paper introduces new algorithms for twisted multiline queues that project to TASEP and TAZRP models, generalizing and connecting previous algorithms, and providing a novel approach for bosonic queues.

Contribution

It generalizes existing algorithms for TASEP and TAZRP using twisted multiline queues, including a novel algorithm for bosonic queues and a Markov process intertwining with symmetric group actions.

Findings

Algorithms project to TASEP and TAZRP models.

Fermionic algorithm generalizes Ferrari-Martin and matches Arita-Ayyer-Mallick-Prolhac.

Bosonic algorithm is new and extends Kuniba-Maruyama-Okado.

Abstract

We define an algorithm on fermionic and bosonic twisted multiline queues that projects to the multispecies totally asymmetric simple exclusion process (TASEP) and the totally asymmetric zero range process (TAZRP) on a ring, respectively. Our algorithm on fermionic multiline queues generalizes the Ferrari-Martin algorithm for TASEP, and we show it is equivalent to the algorithm of Arita-Ayyer-Mallick-Prolhac (2011). Our algorithm on bosonic multiline queues is novel and generalizes the corresponding algorithm of Kuniba-Maruyama-Okado (2016) for the TAZRP. We also define a Markov process on bosonic twisted multiline queues that projects to the TAZRP and intertwines with the symmetric group action on the rows of the multiline queues.