A tightness criterion for random fields, with application to the Ising model

Furlan, Marco; Mourrat, Jean-Christophe

Furlan, Marco; Mourrat, Jean-Christophe (2017), A tightness criterion for random fields, with application to the Ising model, Electronic Journal of Probability, 22, 2017, p. paper no. 97, 29 p.. 10.1214/17-EJP121

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Article accepté pour publication ou publié

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https://hal.archives-ouvertes.fr/hal-01615515

Date

2017

Nom de la revue

Electronic Journal of Probability

Volume

Numéro

2017

Éditeur

Institute of Mathematical Statistics

Pages

paper no. 97, 29 p.

Identifiant publication

10.1214/17-EJP121

Métadonnées

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Auteur(s)

Furlan, Marco
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Mourrat, Jean-Christophe
Laboratoire d'Analyse, Topologie, Probabilités [LATP]

Résumé (EN)

We present a criterion for a family of random distributions to be tight in local Hölder and Besov spaces of possibly negative regularity on general domains. We then apply this criterion to find the sharp regularity of the magnetization field of the two-dimensional Ising model at criticality, answering a question of [CGN15].

Mots-clés

tightness criterion; local Besov spaces; Ising model