Related papers: Uniform amenability at infinity

We characterize convex cocompact subgroups of the mapping class group of a surface in terms of uniform convergence actions on the zero locus of the limit set. We also construct subgroups that act as uniform convergence groups on their limit…

It is known that exactness for a discrete group is equivalent to C*-exactness, i.e., the exactness of its reduced C*-algebra. The problem of whether this equivalence holds for general locally compact groups has recently been reduced by Cave…

The additivity with respect to exact sequences is notoriously a fundamental property of the algebraic entropy of group endomorphisms. It was proved for abelian groups by deeply exploiting their structure. On the other hand, a solvable…

We provide an alternative proof for the extreme amenability of the unitary group of the hyperfinite II${}_1$-factor von Neumann algebra, endowed with the strong operator topology.

In this paper, we consider the problem of approximating the spectral distribution for a class of random operators over sofic groups. For this purpose, we make use of the concept of locally and empirically converging measures defined by…

We introduce the notions of u-amenability and hyper-u-amenability for countable Borel equivalence relations, strong forms of amenability that are implied by hyperfiniteness. We show that treeable, hyper-u-amenable countable Borel…

In this paper, we introduce the notions of pre-uniform spaces and pre-proximities and investigate some basic properties about them, where the definition of pre-uniformity here is different with the pre-uniformities which are studied in…

We define and study the class of inner ultrahomogeneous groups, which includes Hall's universal group and the universal locally recursively presentable group. We provide simple criteria for ample generic automorphisms, straight maximality,…

In this work we introduce and study a new notion of amenability for actions of locally compact groups on $C^*$-algebras. Our definition extends the definition of amenability for actions of discrete groups due to Claire…

We introduce the notion of first order amenability, as a property of a first order theory $T$: every complete type over $\emptyset$, in possibly infinitely many variables, extends to an automorphism-invariant global Keisler measure in the…

We provide a quantitative formulation of the equivalence between hyperlinearity and soficity for amenable groups, showing that every hyperlinear approximation to such a group is essentially produced from a sofic approximation. This…

Let $G$ be a second countable locally compact groupoid equipped with a Haar system $\lambda$.In this work, we introduce and develop the notion of amenability for continuous unitary representations of $G$, formulated in terms of Hilbert…

We introduce the property of having good subgroups for actions of countable discrete groups on compact metrizable spaces, and show that it implies comparison when the acting group is amenable. As a consequence, free actions on…

Given a finitely generated amenable group we consider ergodic random Schr\"odinger operators on a Cayley graph with random potentials and random boundary conditions. We show that the normalised eigenvalue counting functions of finite volume…

Strongly bounded groups are those groups for which every action by isometries on a metric space has orbits of finite diameter. Many groups have been shown to have this property, and all the known infinite examples so far have cardinality at…

We show that the topology of uniform convergence on bounded sets is compatible with the group law of the automorphism group of a large class of spaces that are endowed with both a uniform structure and a bornology, thus yielding numerous…

The superconvergence phenomenon is shown for products of free, identically distributed random variables. We also show that a certain Holder regularity, first demonstrated by Biane for the density of a free additive convolution with a…

A new flavour of amenability for discrete semigroups is proposed that generalises group amenability and follows from a \Folner-type condition. Some examples are explored, to argue that this new notion better captures some essential ideas of…

An equivalent condition for the product of elements of an independent random sample on a compact algebraic group converging in distribution to some random variable as the sample size increases is obtained. Namely, a limit distribution…

We prove that amenability of a unitary co-representation $U$ of a locally compact quantum group passes to unitary co-representations that weakly contain $U$. This generalizes a result of Bekka, and answers affirmatively a question of…