Volume 25, 2021
|Page(s)||433 - 459|
|Published online||15 November 2021|
Unit boundary length quantum disk: a study of two different perspectives and their equivalence
Département de mathématiques de l’ENS de Lyon,
15 parvis René Descartes,
* Corresponding author: firstname.lastname@example.org
Accepted: 21 October 2021
The theory of the two-dimensional Liouville Quantum Gravity, first introduced by Polyakov in his 1981 work has become a key notion in the study of random surfaces. In a series of articles, David, Huang, Kupiainen, Rhodes and Vargas, on the one hand, and Duplantier, Miller and Sheffield on the other hand, investigated this topic in the realm of probability theory, and both provided definitions for fundamentals objects of the theory: the unit area quantum sphere and the unit boundary length quantum disk. In a recent article, Aru, Huang and Sun showed that the definitions given in the case of the sphere coincide. We study here the two different perspectives provided for the unit boundary length quantum disk and show that they define the same probabilistic objects by considering two similar limiting procedures giving rise to them.
Mathematics Subject Classification: 60D05 / 81T20 / 81T40
Key words: Liouville Quantum Gravity / Gaussian Free Field / Gaussian Multiplicative Chaos
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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