A characterisation of the continuum Gaussian free field in arbitrary dimensions
[Une caractérisation du champ libre gaussien dans le continu en toute dimension]
Aru, Juhan1 ; Powell, Ellen2
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, Tome 9 (2022), pp. 1101-1120.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/jep.201
Classification : 60G15, 60G60, 60J65
Keywords: Gaussian free field, Gaussian fields, Markov property, Brownian motion, characterisation theorem
Mot clés : Champ libre gaussien, champs gaussiens, propriété de Markov, mouvement brownien, théorème de caractérisation
Aru, Juhan 1 ; Powell, Ellen 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 
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Aru, Juhan; Powell, Ellen. A characterisation of the continuum Gaussian free field in arbitrary dimensions. Journal de l’École polytechnique — Mathématiques, Tome 9 (2022), pp. 1101-1120. doi : 10.5802/jep.201. http://www.numdam.org/articles/10.5802/jep.201/

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