(1 + ε) moments suffice to characterise the GFF

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dc.contributor.authorBerestycki, Nathanaël
dc.contributor.authorPowell, Ellen
dc.contributor.authorRay, Gourab
dc.date.accessioned2025-02-19T19:44:05Z
dc.date.available2025-02-19T19:44:05Z
dc.date.issued2021
dc.description.abstractWe show that there is “no stable free field of index α∈ (1,2)”, in the following sense. It was proved in [4] that subject to a fourth moment assumption, any random generalised function on a domain D of the plane, satisfying conformal invariance and a natural domain Markov property, must be a constant multiple of the Gaussian free field. In this article we show that the existence of (1+𝜀) moments is sufficient for the same conclusion. A key idea is a new way of exploring the field, where (instead of looking at the more standard circle averages) we start from the boundary and discover averages of the field with respect to a certain “hitting density” of Itô excursions.
dc.description.reviewstatusReviewed
dc.description.scholarlevelFaculty
dc.description.sponsorshipNathanaël Berestycki is supported in part by EPSRC grant EP/L018896/1, the University of Vienna, and FWF grant “Scaling limits in random conformal geometry”. Gourab Ray is supported in part by NSERC 50311-57400 and University of Victoria start-up 10000-27458.
dc.identifier.citationBerestycki, N., Powell, E., & Ray, G. (2021). (1+𝜀) moments suffice to characterise the GFF. Electronic Journal of Probability, 26. https://doi.org/10.1214/20-ejp566
dc.identifier.urihttps://doi.org/10.1214/20-ejp566
dc.identifier.urihttps://hdl.handle.net/1828/21221
dc.language.isoen
dc.publisherElectronic Journal of Probability
dc.rightsAttribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectGaussian free field
dc.subjectcharacterisation
dc.subjectharness
dc.subjectexcursion measure
dc.subjectmoments
dc.title(1 + ε) moments suffice to characterise the GFF
dc.typeArticle

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