Equivalence of Liouville measure and Gaussian free field
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Author(s)
Berestycki, Nathanaël
Sheffield, Scott
Sun, Xin
Date Issued
May 1, 2023
Journal
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
Publisher
Institute of Mathematical Statistics
Citation
Nathanaël Berestycki. Scott Sheffield. Xin Sun. "Equivalence of Liouville measure and Gaussian free field." Ann. Inst. H. Poincaré Probab. Statist. 59 (2) 795 - 816, May 2023.
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Final published version
Abstract
Given an instance h of the Gaussian free field on a planar domain D and a constant γ∈(0,2)Liouville quantum gravity area measure μ:=e^(γh(z)) dzh a.s. determines the measure μ_hh is measurably determined by μ_h Aendowed with a Frostman measure σ whose support is A(independent of h), a Gaussian multiplicative chaos measure μ_(σ,h)can be constructed. We give a mild condition on (A,σ)under which μ_(σ,h)determines h restricted to AAσ such as scale invariance, and hence may be of independent interest.
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DOI of Published Version
https://doi.org/10.1214/22-aihp1280
