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arXiv · 2204.09427

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

Friedrich Martin Schneider
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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.

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Friedrich Martin Schneider. 2023-05-15. Concentration of invariant means and dynamics of chain stabilizers in continuous geometries. https://doi.org/10.1007/s00039-023-00651-w

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