Fluctuations, large deviations and rigidity in hyperuniform systems: a brief survey

TL;DR

This paper surveys fluctuations and large deviations in hyperuniform systems, exploring their rigidity properties and providing conditions for rigidity in one and two dimensions.

Contribution

It offers a concise overview of hyperuniform systems' fluctuation behavior and establishes new criteria for their rigidity in low dimensions.

Findings

Hyperuniform systems exhibit subextensive variance growth.

Sufficient conditions for rigidity in 1D and 2D are provided.

The relation between hyperuniformity and rigidity is clarified.

Abstract

We present a brief survey of fluctuations and large deviations of particle systems with subextensive growth of the variance. These are called hyperuniform (or superhomogeneous) systems. We then discuss the relation between hyperuniformity and rigidity. In particular we give sufficient conditions for rigidity of such systems in d=1,2.