The geodesics in Liouville quantum gravity are not Schramm–Loewner evolutions

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

9 Scopus Citations
View graph of relations



Original languageEnglish
Pages (from-to)677-709
Journal / PublicationProbability Theory and Related Fields
Issue number3-4
Online published21 Dec 2019
Publication statusPublished - Aug 2020
Externally publishedYes



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.

Research Area(s)

Download Statistics

No data available