Planarity and non-separating cycles in uniform high genus quadrangulations

• 成果类型: Article
• 署名作者: Louf, Baptiste
• 署名单位: Uppsala University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-021-01050-8
• 发表日期: 2022
• 页码: 1183-1206
• 关键词: rooted maps; SURFACES; GROWTH; trees; plane; limit

摘要

We study large uniform random bipartite quadrangulations whose genus grows linearly with the number of faces. Their local convergence was recently established by Budzinski and the author [9, 10]. Here we study several properties of these objects which are not captured by the local topology. Namely we show that balls around the root are planar with high probability up to logarithmic radius, and we prove that there exist non-contractible cycles of constant length with positive probability.