Abstract: The study of random maps has progressed considerably in the past decades, yet the methods used to study them break down when considering graph classes. We advance in this direction by proving Gromov-Hausdorff-Prokhorov convergence and local convergence of random elements of the class of cubic planar graphs, where each vertex has degree 3. Our main result establishes for the first time the Brownian sphere as scaling limit of a model of random graphs that are not embedded into the plane. The approach constructs a connection between the graph distance and a first-passage-percolation distance on the 3-connected core. We believe this method to be helpful in understanding the geometry of further classes of non-embedded planar graphs.
Limits of random cubic planar graphs
04.05.2023 14:00 - 16:00
Organiser:
M. Lis
Location: