18 citations · 91 across the 28 of their papers we have counts for
28 papers
Whirliness beyond amenability
Yannik Höll, Friedrich Martin Schneider
Given a non-atomic standard probability space , we exhibit examples of non-amenable closed topological subgroups of whose natural near-action on …
Amenability and skew-amenability of actions of topological groups
Vadim Alekseev, Hiroshi Ando, Friedrich Martin Schneider +1
We define and study notions of amenability and skew-amenability of continuous actions of topological groups on compact topological spaces. Our main motivation is the question under…
On invariant means and pre-syndetic subgroups
Vladimir G. Pestov, Friedrich Martin Schneider
Beyond the locally compact case, equivalent notions of amenability diverge, and some properties no longer hold, for instance amenability is not inherited by topological subgroups.…
Amenable equivalence relations, Kesten's property, and measurable lamplighters
Maksym Chaudkhari, Kate Juschenko, Friedrich Martin Schneider
We prove a characterization of the amenability of countable Borel equivalence relations in terms of the uniform Liouville property for group actions on their classes. Furthermore,…
Group von Neumann algebras, inner amenability, and unit groups of continuous rings
Friedrich Martin Schneider
We prove that, if a discrete group is not inner amenable, then the unit group of the ring of operators affiliated with the group von Neumann algebra of is non-amenable with…
Intrinsic Dimension for Large-Scale Geometric Learning
Maximilian Stubbemann, Tom Hanika, Friedrich Martin Schneider
The concept of dimension is essential to grasp the complexity of data. A naive approach to determine the dimension of a dataset is based on the number of attributes. More sophistic…
An Application of Farkas' Lemma to Finite-Valued Constraint Satisfaction Problems over Infinite Domains
Friedrich Martin Schneider, Caterina Viola
We show a universal algebraic local characterisation of the expressive power of finite-valued languages with domains of arbitrary cardinality and containing arbitrary many cost fun…
Concentration of invariant means and dynamics of chain stabilizers in continuous geometries
Friedrich Martin Schneider
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 appli…
Entropy of group actions beyond uniform lattices
Till Hauser, Friedrich Martin Schneider
Entropy of measure preserving or continuous actions of amenable discrete groups allows for various equivalent approaches. Among them are the ones given by the techniques developed…
Skew-amenability of topological groups
Kate Juschenko, Friedrich Martin Schneider
We study skew-amenable topological groups, i.e., those admitting a left-invariant mean on the space of bounded real-valued functions left-uniformly continuous in the sense of Bourb…
Concentration of measure, classification of submeasures, and dynamics of
Friedrich Martin Schneider, Sławomir Solecki
Exhibiting a new type of measure concentration, we prove uniform concentration bounds for measurable Lipschitz functions on product spaces, where Lipschitz is taken with respect to…
The Liouville property and random walks on topological groups
Friedrich Martin Schneider, Andreas Thom
We study harmonic functions and Poisson boundaries for Borel probability measures on general (i.e., not necessarily locally compact) topological groups, and we prove that a second-…
Intrinsic dimension and its application to association rules
Tom Hanika, Friedrich Martin Schneider, Gerd Stumme
The curse of dimensionality in the realm of association rules is twofold. Firstly, we have the well known exponential increase in computational complexity with increasing item set…
Equivariant dissipation in non-archimedean groups
Friedrich Martin Schneider
We prove that, if a topological group has an open subgroup of infinite index, then every net of tight Borel probability measures on UEB-converging to invariance dissipates…
Intrinsic Dimension of Geometric Data Sets
Tom Hanika, Friedrich Martin Schneider, Gerd Stumme
The curse of dimensionality is a phenomenon frequently observed in machine learning (ML) and knowledge discovery (KD). There is a large body of literature investigating its origin…
Equivariant concentration in topological groups
Friedrich Martin Schneider
We prove that, if is a second-countable topological group with a compatible right-invariant metric and is a sequence of compactly supported Bor…
MacWilliams' extension theorem for infinite rings
Friedrich Martin Schneider, Jens Zumbrägel
Finite Frobenius rings have been characterized as precisely those finite rings satisfying the MacWilliams extension property, by work of Wood. In the present note we offer a genera…
About von Neumann's problem for locally compact groups
Friedrich Martin Schneider
We note a generalization of Whyte's geometric solution to the von Neumann problem for locally compact groups in terms of Borel and clopen piecewise translations. This strengthens a…
On amenability and groups of measurable maps
Vladimir G. Pestov, Friedrich Martin Schneider
We show that if is an amenable topological group, then the topological group of strongly measurable maps from into endowed with the topology of conve…
On Følner sets in topological groups
Friedrich Martin Schneider, Andreas Thom
We extend Følner's amenability criterion to the realm of general topological groups. Building on this, we show that a topological group is amenable if and only if its left tran…
A uniform Birkhoff theorem
Friedrich Martin Schneider
Garret Birkhoff's HSP theorem characterizes the classes of models of algebraic theories as those being closed with respect to homomorphic images, subalgebras, and products. In part…
Every simple compact semiring is finite
Friedrich Martin Schneider, Jens Zumbrägel
A Hausdorff topological semiring is called simple if every non-zero continuous homomorphism into another Hausdorff topological semiring is injective. Classical work by Anzai and Ka…
A topological characterisation of endomorphism monoids of countable structures
Manuel Bodirsky, Friedrich Martin Schneider
A topological monoid is isomorphic to an endomorphism monoid of a countable structure if and only if it is separable and has a compatible complete ultrametric such that composition…
Topological Entropy of Formal Languages
Friedrich Martin Schneider, Daniel Borchmann
We introduce the notion of topological entropy of a formal languages as the topological entropy of the minimal topological automaton accepting it. Using a characterization of this…