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

Aru, Juhan; Papon, Léonie; Powell, Ellen

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
• 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