A characterisation of the Gaussian free field

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.

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Bibliographic Details
Published inProbability theory and related fields Vol. 176; no. 3-4; pp. 1259 - 1301
Main Authors Berestycki, Nathanaël, Powell, Ellen, Ray, Gourab
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2020
Springer Nature B.V
Subjects
Economics
Finance
Insurance
Management
Markov processes
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Probability
Probability Theory and Stochastic Processes
Quantitative Finance
Statistics for Business
Theoretical
60G60
60K35
60G15
60J67
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-019-00939-9