Type $C$ multiline queues and the open-boundary TASEP

Olya Mandelshtam; Jerónimo Valencia-Porras

Type $C$ multiline queues and the open-boundary TASEP

Combinatorics 2026-07-27 v1 Probability

Authors: Olya Mandelshtam , Jerónimo Valencia-Porras

Abstract

The totally asymmetric simple exclusion process (TASEP) with open boundaries is a finite Markov chain describing particles hopping between adjacent sites on a one-dimensional lattice with left and right boundary transitions governed by parameters $\alpha$ and $\beta$ . The multispecies TASEP is a higher-rank generalization in which particles have different species. Multiline queues were introduced by Ferrari and Martin (2007) to compute the stationary distribution of the multispecies TASEP on a circle. It has remained an open problem to find a combinatorial formula for the stationary distribution of the multispecies open-boundary TASEP. Using Kirillov--Reshetikhin crystals of type $C$ , we construct type $C$ multiline queues and a corresponding Ferrari--Martin pairing algorithm that projects them to TASEP configurations. This yields a combinatorial formula for the stationary distribution of the multispecies open-boundary TASEP for the $\alpha=\beta=1$ specialization.

Cite

@article{arxiv.2607.24637,
  title  = {Type $C$ multiline queues and the open-boundary TASEP},
  author = {Olya Mandelshtam and Jerónimo Valencia-Porras},
  journal= {arXiv preprint arXiv:2607.24637},
  year   = {2026}
}