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The $(q,\mu,\nu)$-Boson process and $(q,\mu,\nu)$-TASEP
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abstract
We prove a intertwining relation (or Markov duality) between the $(q,\mu,\nu)$-Boson process and $(q,\mu,\nu)$-TASEP, two discrete time Markov chains introduced by Povolotsky. Using this and a variant of the coordinate Bethe ansatz we compute nested contour integral formulas for expectations of a family of observables of the $(q,\mu,\nu)$-TASEP when started from step initial data. We then utilize these to prove a Fredholm determinant formula for distribution of the location of any given particle.
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Cited by 1 Pith paper
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The boundary-driven multispecies harmonic process
A multispecies harmonic process with boundary reservoirs is introduced and proven Yang-Baxter integrable via a factorized R-matrix and open-chain K-matrices, with three dual processes.
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