A short proof of a symmetry identity for the q-Hahn distribution

Guillaume Barraquand (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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 Corwin in "The q-Hahn Boson Process and q-Hahn TASEP", Int. Math. Res. Not., 2014, 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.

Domaines: Probabilités [math.PR]; Combinatoire [math.CO]

Guillaume Barraquand. A short proof of a symmetry identity for the q-Hahn distribution. Electronic Communications in Probability, 2014, 19 (50), pp.1-3. ⟨10.1214/ECP.v19-3674⟩. ⟨hal-01108348⟩