Related papers: On Mixing of Staircase Transformations
We show that there is a rank 1 transformation that is mildly mixing but does not have minimal self-joinings, answering a question of Thouvenot.
In this paper, we study topological properties of the right action by translation of the Weyl Chamber flow on the space of Weyl chambers. We obtain a necessary and sufficient condition for topological mixing. (1)
We prove that there exists a topologically mixing homeomorphism which is completely scrambled. We also prove that for any integer $n\geq 1$ there is a continuum of topological dimension $n$ supporting a transitive completely scrambled…
We develop a method to study sufficient conditions for perfect mixed tilings. Our framework allows the embedding of bounded degree graphs $H$ with components of sublinear order. As a corollary, we recover and extend the work of K\"uhn and…
We give sufficient conditions ensuring that a $\psi$-mixing property holds for the sequence of empirical CDFs associated to a conjugate process.
Stratified spin-up experiments in enclosed cylinders have reported the presence of small pockets of well-mixed fluids but quantitative measurements of the mixedness of the fluid has been lacking. Previous numerical simulations have not…
In this paper we obtain new sufficient conditions for representation of a function as an absolutely convergent Fourier integral. Unlike those known earlier, these conditions are given in terms of belonging to weighted spaces. Adding weights…
We consider completely irrational nilflows on any nilmanifold of step at least $2$. We show that there exists a dense set of smooth time-changes such that any time-change in this class which is not measurably trivial gives rise to a mixing…
The necessary and suffcient condition for a set of matrices to commute is given and proven.
We study metric versions of transitivity, mixing, and hypercyclicity for continuous maps, based on intersections of the form \( f^{n}(U)\cap B_{\delta}(V)\neq\varnothing. \) We introduce $\delta$-topological transitivity,…
We derive mixing properties for a broad class of Poisson count time series satisfying a certain contraction condition. Using specific coupling techniques, we prove absolute regularity at a geometric rate not only for stationary…
We consider the embedding capacity functions $c_{H_b}(z)$ for symplectic embeddings of ellipsoids of eccentricity $z$ into the family of nontrivial rational Hirzebruch surfaces $H_b$ with symplectic form parametrized by $b\in [0,1)$. This…
Considering a Markov chain defined on a cycle, near-quadratic improvement of mixing is shown when only a subtle perturbation is introduced to the structure and non-reversible transition probabilities are used. More precisely, a mixing time…
We prove that a stationary max--infinitely divisible process is mixing (ergodic) iff its dependence function converges to 0 (is Cesaro summable to 0). These criteria are applied to some classes of max--infinitely divisible processes.
We prove rapid mixing for almost all random walks generated by $m$ translations on an arbitrary nilmanifold under mild assumptions on the size of $m$. For several classical classes of nilmanifolds, we show $m=2$ suffices. This provides a…
In this note we give simple examples of a one-dimensional mixing subshift with positive topological entropy which have two distinct measures of maximal entropy. We also give examples of subshifts which have two mutually singular equilibrium…
We obtain limit shape of perfect matchings on a large class of rail-yard graphs with right boundary condition given by the empty partition, and left boundary condition given by either by a staircase partition with constant density or a…
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…
We define a hierarchy of systems with topological completely positive entropy in the context of continuous countable amenable group actions on compact metric spaces. For each countable ordinal we construct a dynamical system on the…
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…