Existence and uniqueness of the Liouville quantum gravity metric for $\gamma \in (0,2)$

Neyman Seminar
Neyman Seminar
Probability Seminar
Nov 13, 2019 4:00pm to 5:00pm
Location: 
1011 Evans Hall
Status: 
Happening As Scheduled
Liouville quantum gravity (LQG) is in some sense the canonical model of a two-dimensional Riemannian manifold and is defined using the (formal) metric tensor \[ e^{\gamma h(z)} (dx^2 + dy^2)\] where $h$ is an instance of some form of the Gaussian free field and $\gamma \in (0,2)$ is a parameter. This expression does not make literal sense since $h$ is a distribution and not a function, so...
Jason Miller, University of Cambridge