Liouville quantum gravity metrics are not doubling

Simple item page
dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.authorHughes, Liamen_US
dc.contributor.departmentDepartment of Mathematics and Systems Analysisen
dc.contributor.groupauthorMathematical Physicsen
dc.date.accessioned2024-09-04T06:36:43Z
dc.date.available2024-09-04T06:36:43Z
dc.date.issued2024en_US
dc.descriptionPublisher Copyright: © 2024, Institute of Mathematical Statistics. All rights reserved.
dc.description.abstractWe observe that non-doubling metric spaces can be characterized as those that contain arbitrarily large sets of approximately equidistant points and use this to show that, for γ ∈ (0, 2], the γ-Liouville quantum gravity metric is almost surely not doubling and thus cannot be quasisymmetrically embedded into any finite-dimensional Euclidean space. This generalizes the corresponding result of Troscheit [34] for the Brownian map (which is equivalent to the case γ =√8/3).en
dc.description.versionPeer revieweden
dc.format.extent13
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationHughes, L 2024, ' Liouville quantum gravity metrics are not doubling ', Electronic Communications in Probability, vol. 29, 37, pp. 1-13 . https://doi.org/10.1214/24-ECP607en
dc.identifier.doi10.1214/24-ECP607en_US
dc.identifier.issn1083-589X
dc.identifier.otherPURE UUID: ec2361c9-8809-4c01-b580-adebc573ef26en_US
dc.identifier.otherPURE ITEMURL: https://research.aalto.fi/en/publications/ec2361c9-8809-4c01-b580-adebc573ef26en_US
dc.identifier.otherPURE LINK: http://www.scopus.com/inward/record.url?scp=85201282356&partnerID=8YFLogxKen_US
dc.identifier.otherPURE FILEURL: https://research.aalto.fi/files/155976768/Liouville_quantum_gravity_metrics_are_not_doubling.pdfen_US
dc.identifier.urihttps://aaltodoc.aalto.fi/handle/123456789/130637
dc.identifier.urnURN:NBN:fi:aalto-202409046199
dc.language.isoenen
dc.publisherInstitute of Mathematical Statistics
dc.relation.ispartofseriesElectronic Communications in Probability
dc.relation.ispartofseriesVolume 29, pp. 1-13
dc.rightsopenAccessen
dc.subject.keywordAssouad dimensionen_US
dc.subject.keyworddoubling spacesen_US
dc.subject.keywordLiouville quantum gravityen_US
dc.subject.keywordquasisymmetric mapsen_US
dc.titleLiouville quantum gravity metrics are not doublingen
dc.typeA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessäfi
dc.type.versionpublishedVersion
Files
Collections
[article-cris] Perustieteiden korkeakoulu / SCI