Random outerplanar maps and stable looptrees

Jeudi 30 novembre 2017 14:00-15:00 - Sigurður Stefánsson - University of Iceland

Résumé : An outerplanar map is a drawing 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. Caraceni showed that uniform outerplanar maps (all weights equal to 1) with an appropriately rescaled graph distance converge to Aldous’ Brownian tree in the Gromov-Hausdorff sense. This result was generalized by Stufler who showed that the same holds under some moment conditions. I show, in joint work with Stufler, that for certain choices of weights the maps converge towards the alpha-stable looptree, which was recently introduced by Curien and Kortchemski. Our approach relies on the fact that outerplanar maps may be viewed as trees in which each vertex is a dissection of a polygon. Dissections of polygons are further in bijection with trees which allows us to relate the random outerplanar maps to the model of simply generated trees which is understood in detail.

Lieu : salle 117/119 du bâtiment 425

Random outerplanar maps and stable looptrees  Version PDF