A random planar map is a canonical model for a discrete random surface which is studied in probability theory, 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.

# Analysis - Mathematical Physics

## Cardy embedding of random planar maps

### Featuring

Nina Holden

### Speaker Affiliation

ETH Zuerich

### Affiliation

Mathematics

### Event Series

### Video

https://video.ias.edu/analysis/2019/1206-NinaHoldenDate & Time

December 06, 2019 | 3:30 – 4:30pm

### Location

Simonyi Hall 101