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A characterisation of the Gaussian free field

Berestycki, Nathanaël; Powell, Ellen; Ray, Gourab

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Nathanaël Berestycki

Gourab Ray


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.


Berestycki, N., Powell, E., & Ray, G. (2020). A characterisation of the Gaussian free field. Probability Theory and Related Fields, 176(3-4), 1259-1301.

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
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Published Journal Article (Advance online version) (772 Kb)

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Copyright Statement
Advance online version This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution,
and reproduction in any medium, provided you give appropriate credit to the original author(s) and the
source, provide a link to the Creative Commons license, and indicate if changes were made.

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