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August 2019 On thin local sets of the Gaussian free field
Avelio Sepúlveda
Ann. Inst. H. Poincaré Probab. Statist. 55(3): 1797-1813 (August 2019). DOI: 10.1214/19-AIHP1005

Abstract

We study how small a local set of the continuum Gaussian free field (GFF) in dimension $d$ has to be to ensure that this set is thin, which loosely speaking means that it captures no GFF mass on itself, in other words, that the field restricted to it is zero. We provide a criterion on the size of the local set for this to happen, and on the other hand, we show that this criterion is sharp by constructing small local sets that are not thin.

Nous étudions à quel point un ensemble local du champ libre Gaussien (GFF) en dimension $d$ doit être petit pour être sûr que l’ensemble est fin, ce qui signifie informellement que le GFF ne place pas de masse sur l’ensemble, i.e., que le champ restreint a l’ensemble vaut zéro. Nous donnons des critères portant sur la taille de l’ensemble local qui impliquent cette propriété, et par ailleurs nous montrons que ce critère est optimal en construisant des ensembles locaux petits qui ne sont pas fins.

Citation

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Avelio Sepúlveda. "On thin local sets of the Gaussian free field." Ann. Inst. H. Poincaré Probab. Statist. 55 (3) 1797 - 1813, August 2019. https://doi.org/10.1214/19-AIHP1005

Information

Received: 13 March 2017; Revised: 24 May 2018; Accepted: 22 May 2019; Published: August 2019
First available in Project Euclid: 25 September 2019

zbMATH: 07133738
MathSciNet: MR4010952
Digital Object Identifier: 10.1214/19-AIHP1005

Subjects:
Primary: 60D05, 60K35

Rights: Copyright © 2019 Institut Henri Poincaré

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Vol.55 • No. 3 • August 2019
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