# The q-Hahn PushTASEP

### 2018/11/15

(with

Ivan Corwin,

Konstantin Matveev)

arXiv:1811.06475 [math.PR]

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. 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.

The q-Hahn PushTASEP