Logarithmic, Coulomb and Riesz energy of point processes - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

Logarithmic, Coulomb and Riesz energy of point processes

Thomas Leblé

Résumé

We define a notion of logarithmic, Coulomb and Riesz interactions in any dimension for random systems of infinite charged point configurations with a uniform background of opposite sign. We connect this interaction energy with the "renormalized energy" studied by Serfaty et al., which appears in the free energy functional governing the microscopic behavior of logarithmic, Coulomb and Riesz gases. Minimizers of this functional include the Sine-beta processes in the one-dimensional Log-gas case. Using our explicit expression (inspired by the work of Borodin-Serfaty) we prove their convergence to the Poisson process in the high-temperature limit as well as a crystallization result in the low-temperature limit for one-dimensional systems.
Fichier principal
Vignette du fichier
Coulomb_energy_for_point_processes_Leble.pdf (439.41 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03040312 , version 1 (04-12-2020)

Identifiants

  • HAL Id : hal-03040312 , version 1

Citer

Thomas Leblé. Logarithmic, Coulomb and Riesz energy of point processes. 2020. ⟨hal-03040312⟩
19 Consultations
53 Téléchargements

Partager

Gmail Facebook X LinkedIn More