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

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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Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01615515
Date
2017
Journal name
Electronic Journal of Probability
Volume
22
Number
2017
Publisher
Institute of Mathematical Statistics
Pages
paper no. 97, 29 p.
Publication identifier
Metadata
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Author(s)
Furlan, Marco
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Mourrat, Jean-Christophe
Laboratoire d'Analyse, Topologie, Probabilités [LATP]
Abstract (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].
Subjects / Keywords
tightness criterion; local Besov spaces; Ising model