The geodesics in Liouville quantum gravity are not Schramm–Loewner evolutions
Published version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Miller, Jason
Qian, Wei https://orcid.org/0000-0002-4779-4042
Abstract
Abstract: We prove that the geodesics associated with any metric generated from Liouville quantum gravity (LQG) which satisfies certain natural hypotheses are necessarily singular with respect to the law of any type of SLEκ. These hypotheses are satisfied by the LQG metric for γ=8/3 constructed by the first author and Sheffield, and subsequent work by Gwynne and the first author has shown that there is a unique metric which satisfies these hypotheses for each γ∈(0, 2). As a consequence of our analysis, we also establish certain regularity properties of LQG geodesics which imply, among other things, that they are conformally removable.
Description
Funder: University of Cambridge
Keywords
Article, Primary 60D05, Secondary 60J67
Journal Title
Probability Theory and Related Fields
Conference Name
Journal ISSN
0178-8051
1432-2064
1432-2064
Volume Title
177
Publisher
Springer Berlin Heidelberg