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

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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.