A short proof of a symmetry identity for the \(q\)-Hahn distribution. (English) Zbl 1337.60168

Summary: We give a short and elementary proof of a symmetry identity for the \(q\)-moments of the \(q\)-Hahn distribution arising in the study of the \(q\)-Hahn Boson process and the \(q\)-Hahn TASEP. This identity, discovered by I. Corwin in [Int. Math. Res. Not. 2015, No. 14, 5577–5603 (2015; Zbl 1335.82018)], 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.


60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)


Zbl 1335.82018
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