Minor-excluded graphs and soficity
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915547986264064 |
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| author | Solé-Pi, Oriol |
| author_facet | Solé-Pi, Oriol |
| contents | A random rooted graph is said to be sofic if it is the Benjamini-Schramm limit of a sequence of finite graphs. Given any finite graph $H$, we prove that every one-ended, unimodular random rooted graph that does not have H as a minor must be sofic. The hypothesis regarding the number of ends can be dropped under the additional assumption that the graph is quasi-transitive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06731 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minor-excluded graphs and soficity Solé-Pi, Oriol Combinatorics Group Theory Logic Probability 05C83, 60C05, 37A20, 03E15 A random rooted graph is said to be sofic if it is the Benjamini-Schramm limit of a sequence of finite graphs. Given any finite graph $H$, we prove that every one-ended, unimodular random rooted graph that does not have H as a minor must be sofic. The hypothesis regarding the number of ends can be dropped under the additional assumption that the graph is quasi-transitive. |
| title | Minor-excluded graphs and soficity |
| topic | Combinatorics Group Theory Logic Probability 05C83, 60C05, 37A20, 03E15 |
| url | https://arxiv.org/abs/2508.06731 |