Related papers: Rigid actions need not be strongly ergodic

We study a stability property of probability laws with respect to small violations of algorithmic randomness. A sufficient condition of stability is presented in terms of Schnorr tests of algorithmic randomness. Most probability laws, like…

Let $\Gamma$ be a non-elementary Gromov-hyperbolic group, and $\partial \Gamma$ denote its Gromov boundary. We consider $\Gamma$-invariant proper $\delta$-hyperbolic, quasi-convex metric $d$ on $\Gamma$, and the associated…

For a twisted partial action \Theta of a group G on an (associative non-necessarily unital) algebra A over a commutative unital ring k, the crossed product A X_\Theta G is proved to be associative. Given a G-graded k-algebra B =…

We prove that any real-analytic action of $SL(n,\Z), n\ge 3$ with standard homotopy data that preserves an ergodic measure $\mu$ whose support is not contained in a ball, is analytically conjugate on an open invariant set to the standard…

In this paper we study the Poisson process over a $\sigma$-finite measure-space equipped with a measure preserving transformation or a group of measure preserving transformations. For a measure-preserving transformation $T$ acting on a…

The theory of ergodic optimization for distance-expanding maps is extended to Gauss's continued fraction map. Since the set of invariant probability measures is not weak$^*$ closed, we establish a characterisation of the closure of this…

Consider an exact action of discrete group $G$ on a separable $C^*$-algebra $A$. It is shown that the reduced crossed product $A\rtimes_{\sigma, \lambda} G$ is strongly purely infinite - provided that the action of $G$ on any quotient $A/I$…

In this paper we show that the natural action of the symmetric group acting on the product space $\{0, 1 \}^{\mathbb{N}} $ endowed with a symmetric measure is approximately transitive. We also extend the result to a larger class of…

In the variational approach to statistical mechanics, equilibrium states are the rigorous analogues of thermodynamic phases; the question of which invariant measures can arise as equilibrium states is therefore the question of which phases…

We examine some of the properties of uniformly rigid transformations, and analyze the compatibility of uniform rigidity and (measurable) weak mixing along with some of their asymptotic convergence properties. We show that on Cantor space,…

We prove that for a fairly large family of HNN extensions \Gamma, the group measure space II_1 factor L^\infty(X) \rtimes \Gamma given by an arbitrary free ergodic probability measure preserving action of \Gamma, has a unique group measure…

A measure-preserving action of a discrete countable group on a standard probability space is called stable if the associated equivalence relation is isomorphic to its direct product with the ergodic hyperfinite equivalence relation of type…

Given a non-singular action $\Gamma \curvearrowright (X,\mu)$, we define the $*$-algebra $\mathbb C_{\rm fp}[\Gamma \curvearrowright X]$ of operators of finite dynamical propagation associated with this action. This assignment is completely…

The class A of countable groups that admit a faithful, transitive, amenable -- in the sense that there is an invariant mean -- action on a set has been widely investigated in the past. In this paper, we no longer require the action to be…

The article considers generic extensions of measure-preserving actions. We prove that the P-entropy of the generic extensions with finite P-entropy is infinite. This is exploited to obtain the result by Austin, Glasner, Thouvenot, and Weiss…

This is a follow-up to a paper with the same title and by the same authors. In that paper, all groups were assumed to be abelian, and we are now aiming to generalize the results to nonabelian groups. The motivating point is Pedersen's…

This paper studies ergodic properties of certain measures arising in the dynamics of holomorphic correspondences. These measures, in general, are not invariant in the classical sense of ergodic theory. We define a notion of ergodicity, and…

It is known that the Littlewood-Richardson coefficients can be calculated using a certain class of measures, and these measures have a rigidity property when the coefficient is equal to 1. Rigid measures decompose uniquely into sums of…

We investigate the asymptotic structure of (possibly type III) crossed product von Neumann algebras $M = B \rtimes \Gamma$ arising from arbitrary actions $\Gamma \curvearrowright B$ of bi-exact discrete groups (e.g. free groups) on amenable…

Let $G$ be an amenable discrete countable infinite group, $A$ a finite set, and $(\mu_g)_{g\in G}$ a family of probability measures on $A$ such that $\inf_{g\in G}\min_{a\in A}\mu_g(a)>0$. It is shown (among other results) that if the…