Rescaled bipartite planar maps converge to the Brownian map

摘要

For every integer n >= 1, we consider a random planar map M-n which is uniformly distributed over the class of all rooted bipartite planar maps with n edges. We prove that the vertex set of M-n equipped with the graph distance resealed by the factor (2n)(-1/4) converges in distribution, in the Gromov-Hausdorff sense, to the Brownian map. This complements several recent results giving the convergence of various classes of random planar maps to the Brownian map.