Coamenability and cospectral radius for orbit equivalence relations
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910108348317696 |
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| author | Hayes, Ben |
| author_facet | Hayes, Ben |
| contents | We consider inclusions $\mathcal{S}\leq \mathcal{R}$ of discrete, probability measure-preserving orbit equivalence relations. In previous work with Abért-Fraçzyk, we established the pointwise almost sure existence of the cospectral radius of a random walk on the $\mathcal{R}$-classes. In this paper, we investigate the connections of this cospectral radius to the coamenability of the inclusion $\mathcal{S}\leq \mathcal{R}$. We also undertake a systematic study of coamenability for inclusions of relations, establishing several equivalence formulations of this notion. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_16480 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coamenability and cospectral radius for orbit equivalence relations Hayes, Ben Dynamical Systems Functional Analysis Group Theory Operator Algebras Probability We consider inclusions $\mathcal{S}\leq \mathcal{R}$ of discrete, probability measure-preserving orbit equivalence relations. In previous work with Abért-Fraçzyk, we established the pointwise almost sure existence of the cospectral radius of a random walk on the $\mathcal{R}$-classes. In this paper, we investigate the connections of this cospectral radius to the coamenability of the inclusion $\mathcal{S}\leq \mathcal{R}$. We also undertake a systematic study of coamenability for inclusions of relations, establishing several equivalence formulations of this notion. |
| title | Coamenability and cospectral radius for orbit equivalence relations |
| topic | Dynamical Systems Functional Analysis Group Theory Operator Algebras Probability |
| url | https://arxiv.org/abs/2410.16480 |