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The scaling limit of random cubic planar graphs

Planar maps are planar graphs embedded in the sphere, seen up to deformation. In recent years, there has been a lot of progress on the study of their large-scale geometry, culminating with the description of their scaling limit: the Brownian map. However, very little is known on the large-scale geometry of random planar graphs, i.e. when the embedding is known to exist but is not specified. We establish the first precise scaling limit result for planar graphs when the vertices have degree three. The limit is shown to also be the Brownian sphere. Joint work with M. Albenque and E. Fusy.