A characterisation of the Gaussian free field

Berestycki, Nathanaël; Powell, Ellen; Ray, Gourab

doi:10.1007/s00440-019-00939-9

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Authors

Nathanaël Berestycki

Dr Ellen Powell ellen.g.powell@durham.ac.uk
Associate Professor

Gourab Ray

Abstract

We prove that a random distribution in two dimensions which is conformally invariant and satisfies a natural domain Markov property is a multiple of the Gaussian free field. This result holds subject only to a fourth moment assumption.

Citation

Berestycki, N., Powell, E., & Ray, G. (2020). A characterisation of the Gaussian free field. Probability Theory and Related Fields, 176(3-4), 1259-1301. https://doi.org/10.1007/s00440-019-00939-9

Journal Article Type	Article
Acceptance Date	Jul 22, 2019
Online Publication Date	Aug 30, 2019
Publication Date	Apr 30, 2020
Deposit Date	Sep 28, 2019
Publicly Available Date	Oct 8, 2019
Journal	Probability Theory and Related Fields
Print ISSN	0178-8051
Electronic ISSN	1432-2064
Publisher	Springer
Peer Reviewed	Peer Reviewed
Volume	176
Issue	3-4
Pages	1259-1301
DOI	https://doi.org/10.1007/s00440-019-00939-9

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