We study the local limits of uniform high genus bipartite maps with prescribed face degrees. We prove the convergence toward 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.
The second author was supported in part by ERC—Stg 716083—“CombiTop.”
The authors would like to thank Omer Angel, Guillaume Chapuy and Nicolas Curien for useful discussions and comments about this work.
"Local limits of bipartite maps with prescribed face degrees in high genus." Ann. Probab. 50 (3) 1059 - 1126, May 2022. https://doi.org/10.1214/21-AOP1554