Juhan Aru
Thick points of the planar GFF are totally disconnected for all γ≠0
Aru, Juhan; Papon, Léonie; Powell, Ellen
Authors
L?Onie Papon leonie.b.papon@durham.ac.uk
Combined Role
Dr Ellen Powell ellen.g.powell@durham.ac.uk
Associate Professor
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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Copyright Statement
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