Geometry of random planar maps with high degrees


For many types of random planar maps, i.e. planar graphs embedded in the sphere, it is known that their geometry possesses a scaling limit described by a universal random continuous metric space known as the Brownian sphere. One way to escape this universality class is to consider random planar maps that harbor vertices of very high degree. In this talk I will describe a peeling exploration that allows us to study distances in such maps. Based on the results we conjecture the existence of a new one-parameter family of random continuous metric spaces, referred to tentatively as the stable spheres.

TU Delft