Electronic Journal of Probability

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

Marco Furlan and Jean-Christophe Mourrat

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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].

Article information

Electron. J. Probab., Volume 22 (2017), paper no. 97, 29 pp.

Received: 2 November 2016
Accepted: 25 October 2017
First available in Project Euclid: 16 November 2017

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Zentralblatt MATH identifier

Primary: 60F17: Functional limit theorems; invariance principles 60G60: Random fields 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

tightness criterion local Besov spaces Ising model

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Furlan, Marco; Mourrat, Jean-Christophe. A tightness criterion for random fields, with application to the Ising model. Electron. J. Probab. 22 (2017), paper no. 97, 29 pp. doi:10.1214/17-EJP121. https://projecteuclid.org/euclid.ejp/1510802251

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