Diffraction Theory of Point Processes: Systems with Clumping and Repulsion

TL;DR

This paper explores the diffraction properties of various point processes, including determinantal, permanental, and Gaussian zero sets, providing explicit calculations of their autocorrelation and diffraction measures.

Contribution

It offers explicit diffraction and autocorrelation formulas for several classes of point processes, enhancing understanding of their spatial structures.

Findings

Explicit autocorrelation measures derived for multiple point processes

Diffraction patterns characterized for determinantal and permanental processes

Zero sets of Gaussian analytic functions analyzed for diffraction properties

Abstract

We discuss several examples of point processes (all taken from Hough, Krishnapur, Peres, Vir\'ag (2009)) for which the autocorrelation and diffraction measures can be calculated explicitly. These include certain classes of determinantal and permanental point processes, as well as an isometry-invariant point process that arises as the zero set of a Gaussian random analytic function.