Scaling limits of random outerplanar maps

22 Mar 2019, 09:30
45m
132:028 (Nordita, Stockholm)

132:028

Nordita, Stockholm

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.

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