Type C multiline queues and the open-boundary TASEP

2026/07/27 by Olya Mandelshtam, Jerónimo Valencia-Porras
#math.CO #math.PR

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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 α and β. 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 α=β=1 specialization.

Citations

• Twisted multiline queues for the steady states of TASEP and TAZRP
• A strange five vertex model and multispecies ASEP on a ring
• Rhombic staircase tableaux and Koornwinder polynomials
• Combinatorics of the 2-species exclusion processes, marked Laguerre\n histories, and partially signed permutations
• On Combinatorial Models for Affine Crystals
• From multiline queues to Macdonald polynomials via the exclusion process
• Stationary distributions of the multi-type ASEP
• Toric tableaux and the inhomogeneous two-species TASEP on a ring
• Rhombic alternative tableaux and assemblées of permutations
• Multi-Catalan Tableaux and the Two-Species TASEP
• A Markov chain on permutations which projects to the PASEP
• Tableaux combinatorics for the asymmetric exclusion process
• A combinatorial approach to jumping particles
• Affine type A crystal structure on tensor products of rectangles, Demazure characters, and nilpotent varieties
• Kostka Polynomials and Energy Functions in Solvable Lattice Models

Related

• Twisted multiline queues for the steady states of TASEP and TAZRP
• From multiline queues to Macdonald polynomials via the exclusion process
• Continuous Multi-line Queues and TASEP
• Toric tableaux and the inhomogeneous two-species TASEP on a ring
• TASEP with a general initial condition and a deterministically moving wall