Zusammenfassung für den Vortrag am 22.09.2020 (11:00 Uhr)Seminar on Nonlinear Algebra
Nina Holden (ETH Zurich, Switzerland / New York University, USA)
Cardy embedding of random planar maps
A random planar map is a canonical model for a discrete random surface which is studied in probability, combinatorics, mathematical physics, and geometry. Liouville quantum gravity is a canonical model for a random 2d Riemannian manifold with roots in the physics literature. In a joint work with Xin Sun we prove a strong relationship between these two natural models for random surfaces. Namely, we prove that the random planar map converges in the scaling limit to Liouville quantum gravity under a discrete conformal embedding which we call the Cardy embedding.