Speaker
Sigurdur Örn Stefansson
(University of Iceland)
Description
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. We study the phase diagram of random outerplanar maps
sampled according to non-negative weights that are assigned
to each face of a map. We prove that for certain choices of
weights the map looks like a rescaled version of its
boundary when its number of vertices tends to infinity. The
properly rescaled outerplanar maps are then shown to
converge (in a precise sense) to the so-called α-stable
looptree introduced by Curien and Kortchemski (2014), with
the parameter α depending on the specific weight-sequence.
