A characterisation of the continuum Gaussian free field in arbitrary dimensions

Aru, Juhan; Powell, Ellen

Abstract

e prove that under certain mild moment and continuity assumptions, the d-dimensional continuum Gaussian free field is the only stochastic process satisfying the usual domain Markov property and a scaling assumption. Our proof is based on a decomposition of the underlying functional space in terms of radial processes and spherical harmonics

Citation

Aru, J., & Powell, E. (2022). A characterisation of the continuum Gaussian free field in arbitrary dimensions. Journal de l’École polytechnique — Mathématiques, 9, 1101-1120. https://doi.org/10.5802/jep.201

• Journal Article Type: Article
• Acceptance Date: Jun 17, 2022
• Online Publication Date: Jun 30, 2022
• Publication Date: 2022
• Deposit Date: Jul 27, 2022
• Publicly Available Date: Jul 27, 2022
• Journal: Journal de l’École polytechnique — Mathématiques
• Print ISSN: 2429-7100
• Electronic ISSN: 2270-518X
• Publisher: École polytechnique
• Peer Reviewed: Peer Reviewed
• Volume: 9
• Pages: 1101-1120
• DOI: https://doi.org/10.5802/jep.201
• Public URL: https://durham-repository.worktribe.com/output/1196785