Radial Toeplitz operators and invariant determinantal point processes on Cayley trees

Abstract

We give a complete description of bounded radial Toeplitz operators on the Hilbert space associated with a Cayley tree. As an application, we give a complete classification of a rich family of determinantal point processes on Cayley trees whose correlation kernels and thus distributions are invariant under the action of the graph automorphisms of the Cayley trees.