The qHahn PushTASEP
Abstract
We introduce the $q$Hahn PushTASEP  an integrable stochastic interacting particle system which is a 3parameter generalization of the PushTASEP, a wellknown 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 (2013). We establish Markov duality relations and contour integral formulas for the $q$Hahn PushTASEP. In a $q\to 1$ limit of our process we arrive at a random recursion which, in a special case, appears to be similar to the inverseBeta polymer model. However, unlike in recursions for Beta polymer models, the weights (i.e., the coefficients of the recursion) in our model depend on the previous values of the partition function in a nontrivial manner.
 Publication:

arXiv eprints
 Pub Date:
 November 2018
 arXiv:
 arXiv:1811.06475
 Bibcode:
 2018arXiv181106475C
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 Mathematics  Combinatorics;
 Mathematics  Quantum Algebra
 EPrint:
 29 pages, 3 figures