Tessellations of random maps of arbitrary genus Grégory Miermont

  title={Tessellations of random maps of arbitrary genus Gr{\'e}gory Miermont},
  author={Gr{\'e}gory Miermont},
We investigate Voronoi-like tessellations of bipartite quadrangulations on surfaces of arbitrary genus, by using a natural generalization of a bijection of Marcus and Schaeffer allowing to encode such structures into labeled maps with a fixed number of faces. We investigate the scaling limits of the latter. Applications include asymptotic enumeration results for quadrangulations, and typical metric properties of randomly sampled quadrangulations. In particular, we show that scaling limits of… CONTINUE READING
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