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

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tightness_revised.pdf (478.4Kb)
Date
2017
Link to item file
https://hal.archives-ouvertes.fr/hal-01615515
Dewey
Probabilités et mathématiques appliquées
Sujet
tightness criterion; local Besov spaces; Ising model
Journal issue
Electronic Journal of Probability
Volume
22
Number
2017
Publication date
10-2017
Article pages
paper no. 97, 29 p.
Publisher
Institute of Mathematical Statistics
DOI
http://dx.doi.org/10.1214/17-EJP121
URI
https://basepub.dauphine.fr/handle/123456789/18496
Collections
  • CEREMADE : Publications
Metadata
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Author
Furlan, Marco
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Mourrat, Jean-Christophe
400941 Laboratoire d'Analyse, Topologie, Probabilités [LATP]
Type
Article accepté pour publication ou publié
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].

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