A Central Limit Theorem for the Number of Degree-k Vertices in Random Maps
We prove that the number of vertices of given degree in (general or 2-connected) random planar maps satisfies a central limit theorem with mean and variance that are asymptotically linear in the number of edges. The proof relies on an analytic version of the quadratic method and singularity analysis of multivariate generating functions.
central limit theorem planar map degree distribution