2017

Liouville quantum gravity as a metric space and a scaling limit

Miller, Jason

Understand

Over the past few decades, two natural random surface models have emerged within physics and mathematics.

  • The first is Liouville quantum gravity, which has its roots in string theory and conformal field theory from the 1980s and 1990s.
  • The second is the Brownian map, which has its roots in planar map combinatorics from the 1960s together with recent scaling limit results.
  • This article surveys a series of works with Sheffield in which it is shown that Liouville quantum gravity (LQG) with parameter $\gamma=\sqrt{8/3}$ is equivalent to the Brownian map.

Reading the bibliography…