Coamenability and cospectral radius for orbit equivalence relations
Abstract
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 equivalent formulations of this notion.
Fields of Study & Subjects
Advanced Topics in Algebra
Advanced Algebra and Geometry
Mathematics and Applications
Publication details
- Journal / source
- Journal of Modern Dynamics
- Volume
- 22
- Issue
- 0
- Pages
- 695–749
- Publication date
- 1 January 2026
- Language
- EN