The \(q\)-Hahn boson process and \(q\)-Hahn TASEP. (English) Zbl 1335.82018

Corwin, Ivan

Int. Math. Res. Not. 2015, No. 14, 5577-5603 (2015).

This paper provides extensions of the \(q\)-Hahn boson process and the \(q\)-Hahn TASEP (totally asymmetric simple exclusion process) and exhibits some features of their mutual relation. A Bethe ansatz is used to compute the expectations of a family of observables of the \(q\)-Hahn TASEP, and a Fredholm determinant formula is proven for the distribution of the location of any given particle.

Reviewer: Guy Jumarie (Montréal)

MSC:

82C22	Interacting particle systems in time-dependent statistical mechanics
82C23	Exactly solvable dynamic models in time-dependent statistical mechanics
60J05	Discrete-time Markov processes on general state spaces

Keywords:

\(q\)-Hahn boson process; \(q\)-Hahn TASEP