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arXiv · 2109.01252

Introduction to the Liouville quantum gravity metric

Jian Ding·Julien Dubedat·Ewain Gwynne
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Abstract

Liouville quantum gravity (LQG) is a one-parameter family of models of random fractal surfaces which first appeared in the physics literature in the 1980s. Recent works have constructed a metric (distance function) on an LQG surface. We give an overview of the construction of this metric and discuss some of its most important properties, such as the behavior of geodesics and the KPZ formula. We also discuss some of the main techniques for proving statements about the LQG metric, give examples of their use, and discuss some open problems.

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Jian Ding, Julien Dubedat, Ewain Gwynne. 2023-02-23. Introduction to the Liouville quantum gravity metric. https://arxiv.org/abs/2109.01252

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