The q-Hahn PushTASEP

Ivan Corwin, Konstantin Matveev, Leonid Petrov

Published 2018-11-15Version 1

We introduce the q-Hahn PushTASEP --- an integrable stochastic interacting particle system which is a 3-parameter generalization of the PushTASEP, a well-known close relative of the TASEP (Totally Asymmetric Simple Exclusion Process). The transition probabilities in the q-Hahn PushTASEP are expressed through the ${}_4\phi_3$ basic hypergeometric function. Under suitable limits, the q-Hahn PushTASEP degenerates to all known integrable (1+1)-dimensional stochastic systems with a pushing mechanism. One can thus view our new system as a pushing counterpart of the q-Hahn TASEP introduced by Povolotsky (arXiv:1308.3250). We establish Markov duality relations and contour integral formulas for the q-Hahn PushTASEP. We also take a $q\to1$ limit of our process arriving at a new beta polymer-like model.