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arXiv · 1707.02663

Toric tableaux and the inhomogeneous two-species TASEP on a ring

Olya Mandelshtam
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Abstract

The inhomogeneous two-species TASEP on a ring is an exclusion process that describes particles of different species hopping clockwise on a ring with parameters giving the hopping rates for different species. We introduce a combinatorial object that we call \emph{toric rhombic alternative tableaux}, which are certain fillings of tableaux on a triangular lattice tiled with rhombi, and are in bijection with the well-studied \emph{multiline queues} of Ferrari and Martin. Using the tableaux, we obtain a formula for the stationary probabilities of this TASEP, which specializes to results of Ayyer and Linusson. We obtain, in addition, an explicit determinantal formula for these probabilities, and define a Markov chain on the tableaux that projects to the two-species TASEP on a ring.

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Olya Mandelshtam. 2017-07-10. Toric tableaux and the inhomogeneous two-species TASEP on a ring. https://arxiv.org/abs/1707.02663

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