Concentration of invariant means and dynamics of chain stabilizers in continuous geometries

Abstract

We prove a concentration inequality for invariant means on topological groups, namely for such adapted to a chain of amenable topological subgroups. The result is based on an application of Azuma's martingale inequality and provides a method for establishing extreme amenability. Building on this technique, we exhibit new examples of extremely amenable groups arising from von Neumann's continuous geometries. Along the way, we also answer a question by Pestov on dynamical concentration in direct products of amenable topological groups.

arXiv comment60 pages, no figures; v2: exposition streamlined, some notation revised, Corollary 1.6 added, 62 pages

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Cited by in corpus (2)

• Group von Neumann algebras, inner amenability, and unit groups of continuous rings
• Hyperlinearity via amenable near representations