Liouville quantum gravity metrics are not doubling
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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2024
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en
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13
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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
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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