Une description de divers aspects du champ libre gaussien dans le continu et de ses analogues discrets définis sur des réseaux, introduisant à des développements sur différents thèmes, notamment la relation entre le champ libre gaussien, les soupes de lacets browniens et les ensembles conformes de boucles CLE4. ©Electre 2024
Lecture notes on the gaussian free field
The Gaussian Free Field (GFF) in the continuum appears to be the natural generalisation of Brownian motion, when one replaces time by a multidimensional continuous parameter. While Brownian motion can be viewed as the most natural random real-valued function defined on R+ with B(0) = 0, the GFF in a domain D of Rd for d ≥ 2 is a natural random real-valued generalised function defined on D with zero boundary conditions on ∂D. In particular, it is not a random continuous function.
The goal of these lecture notes is to describe-some aspects of the continuum GFF and of its discrete counterpart defined on lattices, with the aim of providing a gentle self-contained introduction to some recent developments on this topic, such as the relation between the continuum GFF, Brownian loop-soups and the Conformal Loop Ensembles CLE4.
This is an updated and expanded version of the notes written by the first author (WW) for graduate courses at ETH Zurich (Swiss Federal Institute of Technology in Zürich) in 2014 and 2018. It has benefited from the comments and corrections of students, as well as of a referee ; we thank them all very much. The exercises that are interspersed in the first half of these notes mostly originate from the exercise sheets prepared by the second author (EP) for this course in 2018.
Paru le : 12/05/2022
Thématique : Mathématiques Appliquées
Auteur(s) : Auteur : Wendelin Werner Auteur : Ellen Powell
Éditeur(s) :
Société mathématique de France
Collection(s) : Cours spécialisés
Série(s) : Non précisé.
ISBN : 978-2-85629-952-4
EAN13 : 9782856299524
Reliure : Relié
Pages : 171
Hauteur: 25.0 cm / Largeur 19.0 cm
Épaisseur: 1.4 cm
Poids: 0 g
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