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.

引用

页码：851 / 858

页数：8

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