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arXiv · 1509.09018

Multispecies TASEP and the tetrahedron equation

Atsuo Kuniba·Shouya Maruyama·Masato Okado
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Abstract

We introduce a family of layer to layer transfer matrices in a three-dimensional (3D) lattice model which can be viewed as partition functions of the $q$-oscillator valued six-vertex model on $m \times n$ square lattice. By invoking the tetrahedron equation we establish their commutativity and bilinear relations mixing various boundary conditions. At $q=0$ and $m=n$, they ultimately yield a new proof of the steady state formula for the $n$-species totally asymmetric simple exclusion process (TASEP) obtained recently by the authors, revealing the 3D integrability in the matrix product construction.

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Atsuo Kuniba, Shouya Maruyama, Masato Okado. 2015-09-30. Multispecies TASEP and the tetrahedron equation. https://doi.org/10.1088/1751-8113/49/11/114001

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