Convergence of random planar maps

Samuel S. Watson (Brown)

Abstract :

We will illustrate techniques for proving the convergence of various random planar maps to a continuum random surface called Liouville quantum gravity. Some of these convergence results are with respect to a rather ad hoc topology, but one (the Schnyder wood, also known as a graph realizer) will be with respect to a natural and concrete embedding. Based on joint work with Xin Sun and Yiting Li.