Liouville quantum gravity metrics are not doubling
Loading...
Access rights
openAccess
Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
This publication is imported from Aalto University research portal.
View publication in the Research portal
View/Open full text file from the Research portal
Other link related to publication
View publication in the Research portal
View/Open full text file from the Research portal
Other link related to publication
Author
Date
2024
Major/Subject
Mcode
Degree programme
Language
en
Pages
13
Series
Electronic Communications in Probability, Volume 29, pp. 1-13
Abstract
We 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).Description
Publisher Copyright: © 2024, Institute of Mathematical Statistics. All rights reserved.
Keywords
Assouad dimension, doubling spaces, Liouville quantum gravity, quasisymmetric maps
Other note
Citation
Hughes, 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-ECP607
