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

Abstract

We present a criterion for a family of random distributions to be tight in local Hölder and Besov spaces of possibly negative regularity. We then apply this criterion to the magnetization field of the two-dimensional Ising model at criticality, answering a question of Camia, Garban and Newman.

28 pages. EJP version

References in corpus (1)

• The additive structure of elliptic homogenization

Cited by in corpus (3)

• A Gaussian process related to the mass spectrum of the near-critical Ising model
• Properties of the gradient squared of the discrete Gaussian free field
• The continuum parabolic Anderson model with a half-Laplacian and periodic noise