A bound of the $\beta$-mixing coefficient for point processes in terms of their intensity functions

TL;DR

This paper establishes a general inequality linking the $eta$-mixing coefficients of point processes to their intensity functions, with applications to determinantal point processes demonstrating optimal decay rates.

Contribution

It introduces a novel inequality relating $eta$-mixing coefficients to intensity functions and applies it to determinantal point processes, showing optimal decay rates.

Findings

Derived a general inequality for $eta$-mixing coefficients based on intensity functions

Applied the inequality to determinantal point processes

Proved the decay rate of $eta$-mixing coefficients is optimal for a class of DPPs

Abstract

We prove a general inequality on $\beta$-mixing coefficients of point processes depending uniquely on their $n$-th order intensity functions. We apply this inequality in the case of determinantal point processes and show that the rate of decay of the $\beta$-mixing coefficients of a wide class of DPPs is optimal.