LOCAL LIMITS OF BIPARTITE MAPS WITH PRESCRIBED FACE DEGREES IN HIGH GENUS

• 成果类型: Article
• 署名作者: Budzinski, Thomas; Louf, Baptiste
• 署名单位: Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); Uppsala University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1554
• 发表日期: 2022
• 页码: 1059-1126
• 关键词: brownian map; planar; geodesics

摘要

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.