Related papers: Algorithmic Randomness For Amenable Groups

In the online prediction framework, we use generalized entropy of to study the loss rate of predictors when outcomes are drawn according to stationary ergodic distributions over the binary alphabet. We show that the notion of generalized…

We prove an analog of Rudolph's theorem for actions of countable amenable groups, which asserts that among invariant measures with entropy at least c on the $G$-shift $(\Lambda^G,\sigma)$, a typical measure has entropy $c$ and is Bernoulli.…

This paper introduces and studies a notion of \emph{algorithmic randomness} for subgroups of rationals. Given a randomly generated additive subgroup $(G,+)$ of rationals, two main questions are addressed: first, what are the model-theoretic…

In this paper we study unimodular amenable groups. The first part is devoted to results on the existence of uniform families of epsilon-quasi tilings for these groups. In this context, constructions of Ornstein and Weiss are extended by…

For a locally compact group $G$, let $A^n(G)$ denote the multidimensional Fourier algebra given by $ \otimes_{n}^{eh} A(G).$ This work explores the approximation identity and operator amenability of the algebra $A^n(G)$. Further, we study…

We introduce a notion of algorithmic randomness for algebraic fields. We prove the existence of a continuum of algebraic extensions of $\mathbb{Q}$ that are random according to our definition. We show that there are noncomputable algebraic…

We give an efficient algorithm to randomly generate finitely generated subgroups of a given size, in a finite rank free group. Here, the size of a subgroup is the number of vertices of its representation by a reduced graph such as can be…

We investigate recent uniqueness theorems for reduced $C^*$-algebras of Hausdorff \'{e}tale groupoids in the context of inverse semigroups. In many cases the distinguished subalgebra is closely related to the structure of the inverse…

We say that a countable discrete group $G$ is {\em almost Ornstein} if for every pair of standard non-two-atom probability spaces $(K,\kappa), (L,\lambda)$ with the same Shannon entropy, the Bernoulli shifts $G \cc (K^G,\kappa^G)$ and $G…

We show that the automorphism groups of countably categorical linear orders are extremely amenable. Using methods of Kechris, Pestov, and Todorcevic, we use this fact to derive a structural Ramsey theorem for certain families of finite…

Using tools from the theory of optimal transport, we establish several results concerning isometric actions of amenable topological groups with potentially unbounded orbits. Specifically, suppose $d$ is a compatible left-invariant metric on…

We design, implement and test a simple algorithm which computes the approximate entropy of a finite binary string of arbitrary length. The algorithm uses a weighted average of the Shannon Entropies of the string and all but the last binary…

We show that amenability of a group acting by homeomorphisms can be deduced from a certain local property of the action and recurrency of the orbital Schreier graphs. This covers amenability of a wide class groups, the amenability of which…

We introduce the notion of uniform exactness, or uniform amenability at infinity, for discrete groups and prove it for a wide class of groups containing free groups and their limit groups. This shows a novel strong convergence phenomenon…

Let G be an infinite discrete countable amenable group acting continuously on a Lebesgue space X. In this article, using partition and factor-space, the conditional entropy of the action G is defined. We introduction some properties of…

By classifying $S$-maximal amenable subgroups of algebraic groups over a global field of characteristic zero, we obtain a complete classification of maximal amenable subgroups up to commensurability in the respective arithmetic groups.…

In this paper we extend the approach of M. Cavaleri to effective amenability to the class of computably enumerable groups, i.e. in particular we do not assume that groups are finitely generated. In the case of computable groups we also…

We develop an algorithm for recognizing whether a character belongs to $\Sigma^m$. In order to apply it we just need to know that the ambient group is of type $\mathrm{FP}_m$ or of type $\mathrm{F}_2$ and that the word problem is solvable…

Given a locally finite graph $\Gamma$, an amenable subgroup $G$ of graph automorphisms acting freely and almost transitively on its vertices, and a $G$-invariant activity function $\lambda$, consider the free energy $f_G(\Gamma,\lambda)$ of…

We show that if $G$ is an amenable topological group, then the topological group $L^{0}(G)$ of strongly measurable maps from $([0,1],\lambda)$ into $G$ endowed with the topology of convergence in measure is whirly amenable, hence extremely…