The $(q,\mu ,\nu )$-Boson process and $(q,\mu ,\nu )$-TASEP

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.

18 pages, 2 figures