Non-hyperuniformity of Gibbs point processes with short range interaction

TL;DR

This paper demonstrates that certain Gibbs point processes with short-range interactions are not hyperuniform, under specific stability and range conditions, covering various models like Widom-Rowlinson and Voronoi-based interactions.

Contribution

It establishes the non-hyperuniformity of a broad class of Gibbs point processes with weak dependencies at large distances, under new stability and range assumptions.

Findings

Gibbs point processes with weak long-range dependencies are not hyperuniform.

Results apply to models with superstable, regular, integrable potentials.

Includes models like Widom-Rowlinson and Voronoi-based interactions.

Abstract

We investigate the hyperuniformity of marked Gibbs point processes with weak dependencies among distant points whilst the interactions of close points are kept arbitrary. Some variants of stability and range assumptions are posed on the Papangelou intensity in order to prove that the resulting point process is not hyperuniform. The scope of our results covers many frequently used models including Gibbs point processes with a superstable, lower-regular, integrable pair potential as well as Widom--Rowlinson model with random radii or Gibbs point processes with interactions based on Voronoi tessellation and nearest neighbour graph.