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

2018/12/10 by Jason Miller, Wei Qian, Miller, Jason +1 · 2 citations
Mathematics · Physics and Astronomy · #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #math-ph #math.CV #math.MP #math.PR

paper · pdf · doi:10.48550/arxiv.1812.03913

28 pages and 8 figures

arxiv created 2019/10/16 · arxiv updated 2019/10/17

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.

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