Related papers: Mixing properties of generalized $T, T^{-1}$ trans…
We consider generalized $(T, T^{-1})$ transformations such that the base map satisfies a multiple mixing local limit theorem and anticoncentration large deviation bounds and in the fiber we have $\mathbb{R}^d$ actions with $d=1$ or $2$…
For different classes of measure preserving transformations, we investigate collections of sets that exhibit the property of lightly mixing. Lightly mixing is a stronger property than topological mixing, and requires that a lim inf is…
We study characterizations of ergodicity, weak mixing and strong mixing of W*-dynamical systems in terms of joinings and subsystems of such systems. Ergodic joinings and Ornstein's criterion for strong mixing are also discussed in this…
We study the problem of lifting various mixing properties from a base automorphism $T\in {\rm Aut}\xbm$ to skew products of the form $\tfs$, where $\va:X\to G$ is a cocycle with values in a locally compact Abelian group $G$,…
We prove that a rank one transformation satisfying a condition called restricted growth is a mixing transformation if and only if the spacer sequence for the transformation is uniformly ergodic. Uniform ergodicity is a generalization of the…
We show that some $C^*$--dynamical systems obtained by "quantizing" classical ones on the free Fock space, enjoy very strong ergodic properties. Namely, if the classical dynamical system $(X, T, \m)$ is ergodic but not weakly mixing, then…
Consider a class of skew product transformations consisting of an ergodic or a periodic transformation on a probability space (M, B, m) in the base and a semigroup of transformations on another probability space (W,F,P) in the fibre. Under…
We consider the dynamics of an arbitrary quantum system coupled to a large arbitrary and fully quantum mechanical environment through a random interaction. We establish analytically and check numerically the typicality of this dynamics, in…
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 show that topological mixing, weak mixing and total transitivity are equivalent for coded systems. We provide an example of a mixing coded system which cannot be approximated by any increasing sequence of mixing shifts of finite type,…
This paper considers the egodicity properties in iterated function systems. First, we will introduce chain mixing and chain transitive iterated function systems then some results and examples are presented to compare with these notions in…
We examine the majorization properties of general thermal-like mixed states depending on a set of parameters. Sufficient conditions which ensure the increase in mixedness, and hence of any associated entropic form, when these parameters are…
A technique is presented for multiplexing two ergodic measure preserving transformations together to derive a third limiting transformation. This technique is used to settle a question regarding rigidity of weak mixing transformations.…
Properties of strong mixing have been established for the stationary linear Hawkes process in the univariate case, and can serve as a basis for statistical applications. In this paper, we provide the technical arguments needed to extend the…
Motivated from the study of multiple ergodic average, the investigation of multiplicative shift spaces has drawn much of interest among researchers. This paper focuses on the relation of topologically mixing properties between…
Motivated by work of Dolgopyat and N\'andori, we establish a general method for upgrading limit theorems for Birkhoff sums and cocycles over dynamical systems to mixing limit theorems under mild ergodicity and hyperbolicity assumptions.…
We study ergodic and mixing properties of non-autonomous dynamics on the unit circle generated by inner functions fixing the origin.
We give sufficient conditions ensuring the strong ergodic property of unique mixing for $C^*$-dynamical systems arising from Yang-Baxter-Hecke quantisation. We discuss whether they can be applied to some important cases including monotone,…
We establish an abstract, effective, exponential large deviations type estimate for Markov systems satisfying a weaker form of mixing. We employ this result to derive such estimates, as well as a central limit theorem, for the skew product…
The purpose of this article is twofold. On one hand, we reveal the equivalence of shift of finite type between a one-sided shift $X$ and its associated hom tree-shift $\mathcal{T}_{X}$, as well as the equivalence in the sofic shift. On the…