Talk
Scaling limits of random outerplanar maps
Talk by Prof. Dr. Sigurður Stefánsson
Speaker invited by: Prof. Dr. Valentin Féray
Date: 09.10.17 Time: 14.00 - 14.45 Room: Y27H28
An outerplanar map is an embedding of a planar graph in the sphere which has the property that there is a face in the map such that all the vertices lie on the boundary of that face. A random outerplanar map is defined by assigning non-negative weights to each face of a map. I will show that for certain choices of weights the maps converge in the Gromov-Hausdorff sense towards the alpha-stable looptree, recently introduced by Curien and Kortchemski. Our approach relies on the combinatorial observation that outerplanar maps may be viewed as trees in which each vertex is a further tree. The problem, and the solution, thus relies heavily on the theory of so called simply generated random trees which I will briefly review.
This is a joint work with Benedikt Stufler.