The $(q,μ,ν)$-Boson process and $(q,μ,ν)$-TASEP

We prove a intertwining relation (or Markov duality) between the $(q,μ,ν)$-Boson process and $(q,μ,ν)$-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 $(q,μ,ν)$-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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