A new proof of extreme amenability of the unitary group of the
      hyperfinite II$_1$ factor

Dowerk, Philip A.; Thom, Andreas

doi:10.36045/bbms/1450389251

Cited by 4 publications

(2 citation statements)

References 3 publications

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“…See [29] for more background on this topic. A similar approach was recently carried out in [5] to give a direct proof that the unitary group of the hyperfinite II 1 -factor is extremely amenable. As a by-product, we can give explicit bounds on the concentration function that are useful to give quantitative bounds in various non-commutative Ramsey theoretic applications.…”

Section: No Non-trivial Unitary Representationsmentioning

confidence: 97%

An exotic group as limit of finite special linear groups

Carderi¹,

Thom²

2018

Ann. inst. Fourier

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Section: No Non-trivial Unitary Representationsmentioning

confidence: 97%

An exotic group as limit of finite special linear groups

Carderi¹,

Thom²

2018

Ann. inst. Fourier

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“…In Milman's seminal joint work with Misha Gromov [16], concentration of measure was identified as a source of extreme amenability: if a topological group G contains a directed family of compact subgroups whose union is dense in G and whose normalized Haar measures concentrate in G, then G is extremely amenable. Following the examples of extremely amenable groups discovered in [16], this method has since found numerous further applications [13,12,40,7,5] and extensions [37,9,41,42,48,49].…”

Section: Introductionmentioning

confidence: 99%

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

Schneider¹

2022

Preprint

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

Schneider

2023

Geom. Funct. Anal.

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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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A new proof of extreme amenability of the unitary group of the hyperfinite II$_1$ factor

Cited by 4 publications

References 3 publications

An exotic group as limit of finite special linear groups

An exotic group as limit of finite special linear groups

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

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

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