Related papers: On strong ergodic properties of quantum dynamical …
The paper provides a systematic characterization of quantum ergodic and mixing channels in finite dimensions and a discussion of their structural properties. In particular, we discuss ergodicity in the general case where the fixed point of…
We prove that unital graph C*-algebras often admit a convenient decomposition into amalgamated free products. We use this to give a complete characterization of when a unital graph C*-algebra is residually finite-dimensional and when it is…
Let $\Gamma$ be a countably infinite group. A common theme in ergodic theory is to start with a probability measure-preserving (p.m.p.) action $\Gamma \curvearrowright (X, \mu)$ and a map $f \in L^1(X, \mu)$, and to compare the global…
Let $\varphi:X\to X$ be a homeomorphism of a compact metric space $X$. For any continuous function $F:X\to \mathbb{R}$ there is a one-parameter group $\alpha^{F}$ of automorphisms on the crossed product $C^*$-algebra…
By Bekka's theorem the group C*-algebra of an amenable group $G$ is residually finite dimensional (RFD) if and only if $G$ is maximally almost periodic (MAP). We generalize this result in two directions of dynamical flavour. Firstly, we…
In this paper we present a new characterization of free group actions (in classical differential geometry), involving dynamical systems and representations of the corresponding transformation groups. In fact, given a dynamical system, we…
We study almost sure limiting behavior of extreme and intermediate order statistics arising from strictly stationary sequences. First, we provide sufficient dependence conditions under which these order statistics converges almost surely to…
We introduce the dynamic comparison property for minimal dynamical systems which has applications to the study of crossed product C*-algebras. We demonstrate that this property holds for a large class of systems which includes all examples…
We give a new alternative version of the reconstruction procedure for ergodic actions of compact quantum groups and we refine it to include characterizations of (braided commutative) Yetter-Drinfeld C*-algebras. We then use this to…
We employ an extension of ergodic theory to the random setting to investigate the existence of random periodic solutions of random dynamical systems. Given that a random dynamical system has a dissipative structure, we proved that a random…
We study N interacting random walks on the positive integers. Each particle has drift {\delta} towards infinity, a reflection at the origin, and a drift towards particles with lower positions. This inhomogeneous mean field system is shown…
We give explicit $C^1$-open conditions that ensure that a diffeomorphism possesses a nonhyperbolic ergodic measure with positive entropy. Actually, our criterion provides the existence of a partially hyperbolic compact set with…
It is an old and challenging topic to investigate for which discrete groups G the full group C*-algebra C*(G) is residually finite-dimensional (RFD). In particular not much is known about how the RFD property behaves under fundamental…
In ergodic theory, given sufficient conditions on the system, every weak mixing $\mathbb{N}$-action is strong mixing along a density one subset of $\mathbb{N}$. We ask if a similar statement holds in topological dynamics with density one…
One of the fundamental results of ergodic optimisation asserts that for any dynamical system on a compact metric space $X$ and for any Banach space of continuous real-valued functions on $X$ which embeds densely in $C(X)$ there exists a…
We study invariance of KMS states on graph C*-algebras coming from strongly connected and circulant graphs under the classical and quantum symmetry of the graphs. We show that the unique KMS state for strongly connected graphs is invariant…
Ergodicity is a fundamental requirement for a dynamical system to reach a state of statistical equilibrium. On the other hand, it is known that in slow-fast systems ergodicity of the fast sub- system impedes the equilibration of the whole…
A discrete group $\G$ is called rigidly symmetric if the projective tensor product between the convolution algebra $\ell^1(\G)$ and any $C^*$-algebra $\A$ is symmetric. We show that in each topologically graded $C^*$-algebra over a rigidly…
We consider the properties weak cancellation, K_1-surjectivity, good index theory, and K_1-injectivity for the class of extremally rich C*-algebras, and for the smaller class of isometrically rich C*-algebras. We establish all four…
We give through pseudodifferential operator calculus a proof that the quantum dynamics of a class of infinite harmonic crystals becomes ergodic and mixing with respect to the quantum Gibbs measure if the classical infinite dynamics is…