Institute of Mathematics


Modul:   MAT971  Seminar über stochastische Prozesse

Scaling limits of random maps with prescribed face degrees

Talk by Prof. Dr. Cyril Marzouk

Speaker invited by: Prof. Dr. Jean Bertoin

Date: 10.05.23  Time: 17.15 - 18.45  Room: Y27H12

Random planar maps are toy models in random geometry that allow to easily define discrete random surfaces. One hope that when letting the number of faces tend to infinity and their size to zero at the correct speed, one can get a continuum random surface, in the same way Brownian motion arises from large random walks. A decade ago, after a series of works by different authors, the convergence of random quadrangulations and a few other models to the so-called Brownian map was finally obtained simultaneously by Le Gall and Miermont. In this talk we will discuss the more general model of maps sampled uniformly at random given their face degrees and will discuss the convergence depending on these degrees.