Unimodular random one-ended planar graphs are sofic

被引：1
|
作者：
Timar, Adam [1 ,2 ]
机构：
[1] Univ Iceland, Dept Math, Reykjavik, Iceland
[2] Alfred Renyi Inst Math, Budapest, Hungary
来源：
COMBINATORICS PROBABILITY AND COMPUTING | 2023年 / 32卷 / 06期
基金：
欧洲研究理事会;
关键词：
unimodular random graphs; sofic; Benjamini-Schramm limit; combinatorial embedding;
D O I：
10.1017/S0963548323000159
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We prove that if a unimodular random graph is almost surely planar and has finite expected degree, then it has a combinatorial embedding into the plane which is also unimodular. This implies the claim in the title immediately by a theorem of Angel, Hutchcroft, Nachmias and Ray [2]. Our unimodular embedding also implies that all the dichotomy results of [2] about unimodular maps extend in the one-ended case to unimodular random planar graphs.
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页码：851 / 858
页数：8
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