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Rescaled bipartite planar maps converge to the Brownian map · Around

2013

Rescaled bipartite planar maps converge to the Brownian map

Abraham, Céline

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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.

Built on

Marckert, J.-F., Mokkadem, A
2003
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Bouttier, J., Di Francesco, P., Guitter, E
2004
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Le Gall, J.F
2005
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Pitman, J
2006
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