Exactness and the topology of the space of invariant random equivalence relations
Abstract
Abstract We characterize exactness of a countable group in terms of invariant random equivalence relations (IREs) on . Specifically, we show that is exact if and only if every weak limit of finite IREs is an amenable IRE. In particular, for exact groups, this implies amenability of the restricted rerooting relation associated with the ideal Bernoulli Voronoi tessellation, the discrete analog of the ideal Poisson Voronoi tessellation.
Fields of Study & Subjects
Advanced Topology and Set Theory
Publication details
- Journal / source
- Proceedings of the London Mathematical Society
- Volume
- 132
- Issue
- 5
- Publication date
- 1 May 2026
- Language
- EN