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A characterisation of the continuum Gaussian free field in arbitrary dimensions
Juhan Aru1; Ellen Powell2
1 Institute of Mathematics, École Polytechnique Fédérale de Lausanne CH-1015 Lausanne, Switzerland
2 Department of Mathematical and Computing Sciences, Durham University Upper Mountjoy Campus, Stockton Rd, Durham DH1 3LE, UK
Journal de l’École polytechnique — Mathématiques, Volume 9 (2022), pp. 1101-1120.

We 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.

Nous montrons que, sous de faibles hypothèses de moment et de continuité, le champ libre gaussien dans le continu à d dimensions est le seul processus stochastique satisfaisant à la propriété habituelle de Markov sur le domaine et une propriété d’échelle. Notre preuve est basée sur une décomposition de l’espace fonctionnel sous-jacent en termes de processus radiaux et d’harmoniques sphériques.

Received:
Accepted:
Published online:
DOI: 10.5802/jep.201
Classification: 60G15, 60G60, 60J65
Keywords: Gaussian free field, Gaussian fields, Markov property, Brownian motion, characterisation theorem
Mots-clés : Champ libre gaussien, champs gaussiens, propriété de Markov, mouvement brownien, théorème de caractérisation

Juhan Aru 1; Ellen Powell 2

1 Institute of Mathematics, École Polytechnique Fédérale de Lausanne CH-1015 Lausanne, Switzerland
2 Department of Mathematical and Computing Sciences, Durham University Upper Mountjoy Campus, Stockton Rd, Durham DH1 3LE, UK
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Juhan Aru; Ellen Powell. A characterisation of the continuum Gaussian free field in arbitrary dimensions. Journal de l’École polytechnique — Mathématiques, Volume 9 (2022), pp. 1101-1120. doi : 10.5802/jep.201. https://jep.centre-mersenne.org/articles/10.5802/jep.201/

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