Introduction to the Liouville quantum gravity metric
Probability
2023-02-24 v2 Mathematical Physics
Metric Geometry
math.MP
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.
Cite
@article{arxiv.2109.01252,
title = {Introduction to the Liouville quantum gravity metric},
author = {Jian Ding and Julien Dubedat and Ewain Gwynne},
journal= {arXiv preprint arXiv:2109.01252},
year = {2023}
}
Comments
30 pages, 5 figures. Proceedings of the ICM contribution for 2022