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

• 成果类型: Article
• 署名作者: Miller, Jason; Qian, Wei
• 署名单位: University of Cambridge
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-019-00949-7
• 发表日期: 2020
• 页码: 677-709
• 关键词: GAUSSIAN MULTIPLICATIVE CHAOS; CONVERGENCE; FIELDS; sle

摘要

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 kappa. These hypotheses are satisfied by the LQG metric for gamma = root 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 gamma is an element of (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.