Related papers: Discrete spectrum for amenable group actions

In this paper, we investigate the discrete spectrum of probability measures for actions of locally compact groups. We establish that a probability measure has a discrete spectrum if and only if it has bounded measure-max-mean-complexity. As…

We prove that for certain actions of a discrete countable residually finite amenable group acting on a compact metric space with specification property, periodic measures are dense in the set of invariant measures.

We are interested in dendrites for which all invariant measures of zero-entropy mappings have discrete spectrum, and we prove that this holds when the closure of the endpoint set of the dendrite is countable. This solves an open question…

We show that for ultracontractive irreducible Dirichlet metric measure spaces, the Dirichlet spectrum is discrete for a restriction to any connected open set without any assumption on regularity of the boundary. The main applications…

We say that an action of a countable discrete inverse semigroup on a locally compact Hausdorff space is amenable if its groupoid of germs is amenable in the sense of Anantharaman-Delaroche and Renault. We then show that for a given inverse…

We define spectral gap actions of discrete groups on von Neumann algebras and study their relations with invariant states. We will show that a finitely generated ICC group $\Gamma$ is inner amenable if and only if there exist more than one…

Z.-J. Ruan has shown that several amenability conditions are all equivalent in the case of discrete Kac algebras. In this paper, we extend this work to the case of discrete quantum groups. That is, we show that a discrete quantum group,…

In this note we study countable subgroups of the full group of a measure preserving equivalence relation. We provide various constraints on the group structure, the nature of the action, and on the measure of fixed point sets, that imply…

We show equivalence of pure point diffraction and pure point dynamical spectrum for measurable dynamical systems build from locally finite measures on locally compact Abelian groups. This generalizes all earlier results of this type. Our…

We study dynamical systems which have bounded complexity with respect to three kinds metrics: the Bowen metric $d_n$, the max-mean metric $\hat{d}_n$ and the mean metric $\bar{d}_n$, both in topological dynamics and ergodic theory. It is…

We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which…

We obtain the uniform measure as a stationary measure of the one-dimensional discrete-time quantum walks by solving the corresponding eigenvalue problem. As an application, the uniform probability measure on a finite interval at a time can…

We consider a discrete-time, continuous-state random walk with steps uniformly distributed in a disk of radius of $h$. For a simply connected domain $D$ in the plane, let $\omega_h(0,\cdot;D)$ be the discrete harmonic measure at $0\in D$…

In this paper, we develop spectral analysis of a discrete non-Hermitian quantum system that is a discrete counterpart of some continuous quantum systems on a complex contour. In particular, simple conditions for discreteness of the spectrum…

We study actions of discrete groups on Hilbert $C^*$-modules induced from topological actions on compact Hausdorff spaces. We show non-amenability of actions of non-amenable and non-a-T-menable groups, provided there exists a…

In this paper we introduce the notion of scale pressure and measure theoretic scale pressure for amenable group actions. A variational principle for amenable group actions is presented. We also describe these quantities by pseudo-orbits.…

The distance of a binary operation from being associative can be "measured" by its associative spectrum, an appropriate sequence of positive integers. Particular instances and general properties of associative spectra are studied.

In quantum theory, observables with a continuous spectrum are known to be fundamentally different from those with a discrete and finite spectrum. While some fundamental tests and applications of quantum mechanics originally formulated for…

We initiate the study of a quantitative measure for the failure of a binary operation to be commutative and associative. We call this measure the associative-commutative spectrum as it extends the so-called associative spectrum (also known…

In this article, we define amorphic complexity for actions of locally compact $\sigma$-compact amenable groups on compact metric spaces. Amorphic complexity, originally introduced for $\mathbb Z$-actions, is a topological invariant which…