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arXiv · 1602.07921

Inhomogenous Multispecies TASEP on a ring with spectral parameters

Luigi Cantini
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Abstract

We study an inhomogenous multispecies version of the Totally Asymmetric Simple Exclusion Process (TASEP) on a periodic oriented one dimensional lattice, which depends on two sets of parameters $({\bf \tau},{\bf \nu})$, attached to the particles. After discussing the Yang-Baxter integrability of our model, we study its (unnormalized) stationary measure. Motivated by the integrability of the model we introduce a further set of spectral parameters ${\bf z}$, attached to the sites of the lattice, and we uncover a remarkable underlying algebraic structure. We provide exact formulas for the stationary measure and prove the factorization of the stationary probability of certain configurations in terms of double Schubert polynomials in $({\bf \tau},{\bf \nu})$.

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Luigi Cantini. 2016-02-25. Inhomogenous Multispecies TASEP on a ring with spectral parameters. https://arxiv.org/abs/1602.07921

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