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

Fuente: arXiv
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Main Author: Schneider, Friedrich Martin
Format: Preprint
Published: 2022
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_version_ 1866913210372718592
author Schneider, Friedrich Martin
author_facet Schneider, Friedrich Martin
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2204_09427
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Concentration of invariant means and dynamics of chain stabilizers in continuous geometries
Schneider, Friedrich Martin
Functional Analysis
Group Theory
Rings and Algebras
22A10, 43A07, 06C20, 16E50
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.
title Concentration of invariant means and dynamics of chain stabilizers in continuous geometries
topic Functional Analysis
Group Theory
Rings and Algebras
22A10, 43A07, 06C20, 16E50
url https://arxiv.org/abs/2204.09427