Local limits of bipartite maps with prescribed face degrees in high genus

Thomas Budzinski; Baptiste Louf

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arXiv · 2012.05813

Local limits of bipartite maps with prescribed face degrees in high genus

Thomas Budzinski·Baptiste Louf

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Abstract

We study the local limits of uniform high genus bipartite maps with prescribed face degrees. We prove the convergence towards a family of infinite maps of the plane, the q-IBPMs, which exhibit both a spatial Markov property and a hyperbolic behaviour. Therefore, we observe a similar local behaviour for a wide class of models of random high genus maps, which can be seen as a result of universality. Our results cover all the regimes where the expected degree of the root face remains finite in the limit. This follows a work by the same authors on high genus triangulations arXiv:1902.00492.

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Thomas Budzinski, Baptiste Louf. 2020-12-10. Local limits of bipartite maps with prescribed face degrees in high genus. https://arxiv.org/abs/2012.05813

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