GICAR algebras and dynamics on determinantal point processes: discrete orthogonal polynomial ensemble case

It is known that determinantal point processes have an intimate relation to operator algebras. In the paper, we extend this relationship to encompass dynamical aspects. Especially, we delve into two types of determinantal point processes. One is related to discrete orthogonal polynomials of hypergeometric type, and another is $z$-measures, which arise in the asymptotic representation theory of the symmetric groups. Within the framework of operator algebras, we investigate both unitary and stochastic dynamics on these point processes.