Related papers: Exactness, K-property and infinite mixing
In the context of the long-standing issue of mixing in infinite ergodic theory, we introduce the idea of mixing for observables possessing an infinite-volume average. The idea is borrowed from statistical mechanics and appears to be…
We give a fairly complete characterization of the exact components of a large class of uniformly expanding Markov maps of $\mathbb{R}$. Using this result, for a class of $\mathbb{Z}$-invariant maps and finite modifications thereof, we prove…
In a recent paper, Melbourne and Terhesiu [Operator renewal theory and mixing rates for dynamical systems with infinite measure, Invent. Math. 189 (2012), 61-110] obtained results on mixing and mixing rates for a large class of…
We begin the study of the consequences of the existence of certain infinite matrices. Our present application is to compactness of products of topological spaces.
We analyze a contribution of the finite-width (mass-smearing) effects to the mixing of neutral mesons. It was shown, that this contribution is dominant in the D-meson system and large in the K-meson one. An account of the mass-smearing…
We consider extensions of non-singular maps which are exact, respectively K-mixing, or at least have a decomposition into positive-measure exact, respectively K-mixing, components. The fibers of the extension spaces have countable (finite…
We develop operator renewal theory for flows and apply this to infinite ergodic theory. In particular we obtain results on mixing for a large class of infinite measure semiflows. Examples of systems covered by our results include…
In the scope of the statistical description of dynamical systems, one of the defining features of chaos is the tendency of a system to lose memory of its initial conditions (more precisely, of the distribution of its initial conditions).…
We consider skew products over subshifts of finite type in which the fibers are copies of the real line, and we study their mixing properties with respect to any infinite invariant measure given by the product of a Gibbs measure on the base…
For any infinite zero-density integer set M, we found a rigid measure-preserving transformation mixing along M by answering Bergelson's question. Gaussian and Poisson suspensions over infinite constructions are suggested as suitable…
An analogue of the mixing property of quantum entropy is derived for quantum relative entropy.It is applied to the final state of ideal measurement and to the spectral form of the second density operator. Three cases of states on a directed…
The posterior distribution of the number of components k in a finite mixture satisfies a set of inequality constraints. The result holds irrespective of the parametric form of the mixture components and under assumptions on the prior…
In this survey, we study the relations between amenability (resp. amenability at infinity) of C*-dynamical systems and equality or nuclearity (resp. exactness) of the corresponding crossed products.
An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…
We prove global-local mixing for a large class of dynamical systems with infinite invariant measure. In particular, we treat intermittent maps including maps with multiple neutral fixed points, nonMarkovian intermittent maps, and…
Precision tuning or customized precision number representations is emerging, in these recent years, as one of the most promising techniques that has a positive impact on the footprint of programs concerning energy consumption, bandwidth…
Support for arithmetic in multiple precisions and number formats is becoming increasingly common in emerging high-performance architectures. From a computational scientist's perspective, our goal is to determine how and where we can safely…
We study the properties of `infinite-volume mixing' for two classes of intermittent maps: expanding maps $[0,1] \longrightarrow [0,1]$ with an indifferent fixed point at 0 preserving an infinite, absolutely continuous measure, and expanding…
Characterizations of paracompact finite $C$-spaces via continuous selections are given. We apply these results to obtain some properties of finite $C$-spaces. Factorization theorems and a completion theorem for finite $C$- spaces are also…
This paper extends our earlier results to higher dimensions using a different approach, based on the rigidity of complex structures on certain domains.