Palm measures and rigidity phenomena in point processes

TL;DR

This paper investigates the regularity of Palm measures in point processes, linking it to rigidity-tolerance behavior, and extends existing results to new ensembles like Gaussian analytic function zeros.

Contribution

It introduces a novel connection between Palm measure regularity and rigidity-tolerance, extending prior results to non-determinantal point processes.

Findings

Established the role of rigidity-tolerance in Palm measure regularity

Extended results to Gaussian analytic function zeros

Included new ensembles without determinantal structure

Abstract

We study the mutual regularity properties of Palm measures of point processes, and establish that a key determining factor for these properties is the rigidity-tolerance behaviour of the point process in question (for those processes that exhibit such behaviour). Thereby, we extend the results of Osada-Shirai, Bufetov and Olshanski to new ensembles, particularly those that are devoid of any determinantal structure. These include the zeroes of the standard planar Gaussian analytic function and several others.