A short proof of a symmetry identity for the $(q,\mu ,\nu )$-deformed Binomial distribution

Abstract

We give a short and elementary proof of a $(q,\mu ,\nu )$-deformed Binomial distribution identity arising in the study of the $(q,\mu ,\nu )$-Boson process and the $(q,\mu ,\nu )$-TASEP. This identity found by Corwin in [4] was a key technical step to prove an intertwining relation between the Markov transition matrices of these two classes of discrete-time Markov chains. This was used in turn to derive exact formulas for a large class of observables of both these processes.

3 pages