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May 2022 Local limits of bipartite maps with prescribed face degrees in high genus
Thomas Budzinski, Baptiste Louf
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Ann. Probab. 50(3): 1059-1126 (May 2022). DOI: 10.1214/21-AOP1554

Abstract

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.

Funding Statement

The second author was supported in part by ERC—Stg 716083—“CombiTop.”

Acknowledgments

The authors would like to thank Omer Angel, Guillaume Chapuy and Nicolas Curien for useful discussions and comments about this work.

Citation

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Thomas Budzinski. Baptiste Louf. "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

Information

Received: 1 January 2021; Revised: 1 August 2021; Published: May 2022
First available in Project Euclid: 27 April 2022

Digital Object Identifier: 10.1214/21-AOP1554

Subjects:
Primary: 60C05
Secondary: 05C80

Keywords: higher genus , Local limits , Random maps

Rights: Copyright © 2022 Institute of Mathematical Statistics

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Vol.50 • No. 3 • May 2022
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