The q-Hahn Boson Process and q-Hahn TASEP

Abstract

We prove an intertwining relation (or Markov duality) between the q-Hahn Boson process and q-Hahn TASEP, two discrete time Markov chains introduced by Povolotsky [17], depending on three real parameters q,μ,ν. 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-Hahn 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.