Emmanuel Kammerer (CMAP) A valider Distances on critical O(2) loop-decorated random planar maps
We consider a random planar map coupled with an O(n)-loop model, which
is a graph embedded in the sphere up to deformation together with a
collection of disjoint loops drawn on its faces. Such decorated planar
maps were enumerated recursively by Borot, Bouttier and Guitter using
the so-called gasket decomposition, which consists in cutting out the
regions encircled by loops. The resulting gasket is itself a random map
with large faces, namely a stable map. After a brief overview of the
motivations for studying the geometry of these objects, we will delve
into the asymptotics for distances on the gasket and on the decorated
map in the case n=2.