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

Marco Furlan, Jean Christophe Mourrat

Research output: Contribution to journalArticle

Abstract

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 [8].

Original languageEnglish (US)
Article number97
JournalElectronic Journal of Probability
Volume22
DOIs
StatePublished - 2017

Keywords

  • Ising model
  • Local besov spaces
  • Tightness criterion

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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