Uniform amenability at infinity
Group Theory
2026-05-01 v2 Functional Analysis
Operator Algebras
Abstract
We introduce the notion of uniform exactness, or uniform amenability at infinity, for discrete groups and prove it for a wide class of groups containing free groups and their limit groups. This shows a novel strong convergence phenomenon that any convergent sequence of such groups in the space of marked groups converges strongly in the operator algebraic sense. In particular, convergence of the spectral radius formula is uniform over probability measures on such groups whose supports have a fixed cardinality.
Cite
@article{arxiv.2604.22412,
title = {Uniform amenability at infinity},
author = {Narutaka Ozawa},
journal= {arXiv preprint arXiv:2604.22412},
year = {2026}
}
Comments
20 pages; Introduction improved (v2)