Variance linearity for real Gaussian zeros - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

Variance linearity for real Gaussian zeros

Résumé

We investigate the zero set of a stationary Gaussian process on the real line, and in particular give lower bounds for the variance of the number of points on a large interval, in all generality. We prove that this point process is never hyperuniform, i.e. the variance is at least linear, and give necessary conditions to have linear variance, which are close to be sharp. We study the class of symmetric Bernoulli convolutions and give an example where the zero set is super rigid, weakly mixing, and not hyperuniform.
Fichier principal
Vignette du fichier
zeros-GP copie.pdf (325.22 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02872367 , version 1 (17-06-2020)
hal-02872367 , version 2 (21-07-2020)
hal-02872367 , version 3 (19-10-2021)

Identifiants

Citer

Raphaël Lachièze-Rey. Variance linearity for real Gaussian zeros. 2020. ⟨hal-02872367v1⟩
34 Consultations
126 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More