Excursion decomposition of the 2D continuum GFF - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Excursion decomposition of the 2D continuum GFF

Résumé

In this note we show that the 2D continuum Gaussian free field (GFF) admits an excursion decomposition that is on the one hand similar to the classical excursion decomposition of the Brownian motion, and on the other hand can be seen as an FK representation of the continuum GFF. In particular, 2D continuum GFF can be written as an infinite sum of disjoint positive and negative sign excursions, which are given by Minkowski content measures of clusters of a critical 2D Brownian loop soup with i.i.d. signs. Although the 2D continuum GFF is not even a signed measure, we show that the decomposition to positive and negative parts is unique under natural conditions.
Fichier principal
Vignette du fichier
Aru_Lupu_Sepulveda_2023.pdf (566.53 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04190608 , version 1 (29-08-2023)
hal-04190608 , version 2 (11-10-2023)

Identifiants

Citer

Juhan Aru, Titus Lupu, Avelio Sepúlveda. Excursion decomposition of the 2D continuum GFF. 2023. ⟨hal-04190608v2⟩
20 Consultations
18 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More