Liouville Quantum Gravity on the unit disk
Probability
2017-07-18 v2 Mathematical Physics
Differential Geometry
math.MP
Abstract
Our purpose is to pursue the rigorous construction of Liouville Quantum Field Theory on Riemann surfaces initiated by F. David, A. Kupiainen and the last two authors in the context of the Riemann sphere and inspired by the 1981 seminal work by Polyakov. In this paper, we investigate the case of simply connected domains with boundary. We also make precise conjectures about the relationship of this theory to scaling limits of random planar maps with boundary conformally embedded onto the disk.
Cite
@article{arxiv.1502.04343,
title = {Liouville Quantum Gravity on the unit disk},
author = {Yichao Huang and Rémi Rhodes and Vincent Vargas},
journal= {arXiv preprint arXiv:1502.04343},
year = {2017}
}