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arXiv · 1312.5959

Rescaled bipartite planar maps converge to the Brownian map

Céline Abraham
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Abstract

For every integer $n\geq 1$, we consider a random planar map $\mathcal{M}_n$ which is uniformly distributed over the class of all rooted bipartite planar maps with $n$ edges. We prove that the vertex set of $\mathcal{M}_n$ 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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Céline Abraham. 2013-12-20. Rescaled bipartite planar maps converge to the Brownian map. https://arxiv.org/abs/1312.5959

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