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

Jason Miller; Wei Qian

doi:10.1007/s00440-019-00949-7

Author(s)

Jason Miller
Wei Qian

Detail(s)

Original language	English
Pages (from-to)	677-709
Journal / Publication	Probability Theory and Related Fields
Volume	177
Issue number	3-4
Online published	21 Dec 2019
Publication status	Published - Aug 2020
Externally published	Yes

Link(s)

DOI	DOI https://doi.org/10.1007/s00440-019-00949-7 Final Published version
	Check@CityULib
Attachment(s)	Documents 111409084.pdf Final Published version, 1.22 MB, PDF Publisher's Copyright Statement This full text is made available under CC-BY 4.0. https://creativecommons.org/licenses/by/4.0/
Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-85077156045&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(9a9cc2ba-b23f-422f-9914-df440065e7eb).html

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 SLE_κ. 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.