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

Barraquand, Guillaume

Electron. Commun. Probab. 19, Paper No. 50, 3 p. (2014).

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.

MSC:

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

Keywords:

\(q\)-Hahn process; symmetry; Markov duality

Citations:

Zbl 1335.82018