On estimating the structure factor of a point process, with applications to hyperuniformity - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Statistics and Computing Année : 2023

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

Résumé

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 toolbox structure-factor, containing all the estimators and tools that we discuss.
Fichier principal
Vignette du fichier
sn-article.pdf (3.31 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03615250 , version 1 (22-07-2022)
hal-03615250 , version 2 (27-12-2022)

Identifiants

Citer

Diala Hawat, Guillaume Gautier, Rémi Bardenet, Raphaël Lachièze-Rey. On estimating the structure factor of a point process, with applications to hyperuniformity. Statistics and Computing, 2023. ⟨hal-03615250v2⟩
267 Consultations
142 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More