Rescaled bipartite planar maps converge to the Brownian map

2013/12/20 by Abraham, Céline · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1312.5959

Abstract

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 rescaled 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.

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