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Thick points of the planar GFF are totally disconnected for all γ≠0

Aru, Juhan; Papon, Léonie; Powell, Ellen

Thick points of the planar GFF are totally disconnected for all γ≠0 Thumbnail


Authors

Juhan Aru



Abstract

We prove that the set of γ-thick points of a planar Gaussian free field (GFF) with Dirichlet boundary conditions is a.s. totally disconnected for all γ≠0. Our proof relies on the coupling between a GFF and the nested
CLE4. In particular, we show that the thick points of the GFF are the same as those of the weighted CLE4 nesting field introduced in [24] and establish the almost sure total disconnectedness of the complement of a nested CLE κ∈(8∕3,4]As a corollary we see that the set of singular points for supercritical LQG metrics is a.s. totally disconnected.

Citation

Aru, J., Papon, L., & Powell, E. (2023). Thick points of the planar GFF are totally disconnected for all γ≠0. Electronic Journal of Probability, 28, 1-24. https://doi.org/10.1214/23-ejp975

Journal Article Type Article
Acceptance Date Jun 15, 2023
Online Publication Date Jun 29, 2023
Publication Date Jun 29, 2023
Deposit Date Feb 14, 2024
Publicly Available Date Feb 14, 2024
Journal Electronic Journal of Probability
Electronic ISSN 1083-6489
Publisher Institute of Mathematical Statistics
Peer Reviewed Peer Reviewed
Volume 28
Pages 1-24
DOI https://doi.org/10.1214/23-ejp975
Keywords Statistics, Probability and Uncertainty; Statistics and Probability
Public URL https://durham-repository.worktribe.com/output/2255342

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