Glauber and Kawasaki Dynamics for Determinantal Point Processes in Discrete Spaces

TL;DR

This paper develops Glauber and Kawasaki dynamics for determinantal point processes on discrete spaces, constructing Markov processes that preserve these processes and analyzing their ergodic properties.

Contribution

It introduces a novel construction of Fellerian Markov processes for determinantal point processes in discrete spaces, including their ergodicity analysis.

Findings

Constructed equilibrium Glauber and Kawasaki dynamics for determinantal point processes.

Established the existence of Fellerian Markov processes with specified generators.

Discussed the ergodic behavior of the constructed processes.

Abstract

We construct the equilibrium Glauber and Kawasaki dynamics on discrete spaces which leave invariant certain determinantal point processes. We will construct Fellerian Markov processes with specified core for the generators. Further, we discuss the ergodicity of the processes.