Probability Seminar

Olivier Bernardi (Brandeis)

"Percolation on triangulations, and a bijective path to Liouville quantum gravity"

Abstract:
I will discuss the percolation model on planar triangulations, and present a bijection that is key to relating this model to some fundamental probabilistic objects.  

I will attempt to achieve several goals:

1. Present the site-percolation model on random planar triangulations.
2. Provide an informal introduction to several probabilistic objects: the Gaussian free field, Schramm-Loewner evolutions, and the Brownian map.
3. Present a bijective encoding of percolated triangulations by certain lattice paths, and explain its role in establishing exact relations between the above-mentioned objects.

This is joint work with Nina Holden, and Xin Sun. ​