连续几何中不变均值的集中与链稳定器的动力学

IF 2.4 1区数学 Q1 MATHEMATICS

Geometric and Functional Analysis Pub Date : 2023-10-12 DOI:10.1007/s00039-023-00651-w

Friedrich Martin Schneider

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引用次数: 1

摘要

我们证明了拓扑群上不变均值的一个集中不等式，也就是说，它适用于一个可服从的拓扑子群链。该结果基于Azuma的鞅不等式的一个应用，并提供了一种建立极端可适性的方法。在这项技术的基础上，我们展示了冯·诺依曼连续几何中产生的极易服从群的新例子。在此过程中，我们还回答了Pestov关于服从拓扑群的直积中的动力学集中的问题。

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

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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来源期刊

Geometric and Functional Analysis 数学-数学

CiteScore

3.70

自引率

4.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Geometric And Functional Analysis (GAFA) publishes original research papers of the highest quality on a broad range of mathematical topics related to geometry and analysis. GAFA scored in Scopus as best journal in "Geometry and Topology" since 2014 and as best journal in "Analysis" since 2016. Publishes major results on topics in geometry and analysis. Features papers which make connections between relevant fields and their applications to other areas.