Title :

On estimating the structure factor of a point process, with applications to hyperuniformity

Author(s) :

Hawat, Diala [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Gautier, Guillaume [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Bardenet, Remi [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Lachièze-Rey, Raphaël [Auteur]
Mathématiques Appliquées Paris 5 [MAP5 - UMR 8145]

Journal title :

Statistics and Computing

Publisher :

Springer

Publication date :

2023

ISSN :

1573-1375

HAL domain(s) :

Statistiques [stat]/Méthodologie [stat.ME]
Mathématiques [math]/Probabilités [math.PR]
Physique [physics]/Matière Condensée [cond-mat]
Statistiques [stat]/Calcul [stat.CO]

English abstract : [en]

Hyperuniformity is the study of stationary point processes with a sub-Poisson variance in a large window. In other words, counting the points of a hyperuniform point process that fall in a given large region yields a ...
Show more >Hyperuniformity is the study of stationary point processes with a sub-Poisson variance in a large window. In other words, counting the points of a hyperuniform point process that fall in a given large region yields a small-variance Monte Carlo estimation of the volume. Hyperuniform point processes have received a lot of attention in statistical physics, both for the investigation of natural organized structures and the synthesis of materials. Unfortunately, rigorously proving that a point process is hyperuniform is usually difficult. A common practice in statistical physics and chemistry is to use a few samples to estimate a spectral measure called the structure factor. Its decay around zero provides a diagnostic of hyperuniformity. Different applied fields use however different estimators, and important algorithmic choices proceed from each field’s lore.This paper provides a systematic survey and derivation of known or otherwise natural estimators of the structure factor. We also leverage the consistency of these estimators to contribute the first asymptotically valid statistical test of hyperuniformity. We benchmark all estimators and hyperuniformity diagnostics on a set of examples. In an effort to make investigations of the structure factor and hyperuniformity systematic and reproducible, we further provide the Python toolboxstructure-factor, containing all the estimators and tools that we discuss.Show less >

Language :

Anglais

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL