Scaling limits of random maps in higher genera
Vortrag von Prof. Dr. Grégory Miermont
Sprecher eingeladen von: Prof. Dr. Jean Bertoin
Datum: 20.03.13 Zeit: 17.15 - 19.00 Raum: Y27H25
A map is an embedding of a 2-dimensional graph into a surface, which can be seen as a discrete geometrization of the latter. Therefore, it is natural to view a random map as a discrete random surface, which naturally leads to the question of the existence of a continuum counterpart obtained by passing to the limit after a suitable rescaling of the graph distances in the map. The planar case, where the surface is the 2-dimensional sphere, has been quite thoroughly studied in the past year. In this work in collaboration with Jérémie Bettinelli, we investigate other topologies by characterizing the scaling limits of uniform random plane quadrangulation with a boundary, or uniform bipartite quadrangulations in a closed, compact, orientable surface of fixed genus g. We achieve this by using "surgical" methods, that give a description of the scaling limits in terms of a gluing of elementary planar pieces.