Related papers: Smooth mixing transformations with loosely Bernoul…
In this work we prove sufficient conditions for the Glauber dynamics corresponding to a sequence of (non-product) measures on finite product spaces to be rapidly mixing, i.e. that the mixing time with respect to the total variation distance…
Anomalies in several short-baseline neutrino oscillation experiments suggest the possible existence of sterile neutrinos at about eV scale having appreciable mixing with the already known three neutrinos. We find that if such a light…
The well-known ergodic hierarchy of sheerly ergodic, mixing, Kolmogorov and Bernoulli systems, with each next level supposedly encompassing the previous one, is shown to be too simplistic in its usual formulation. A K-system can be sheerly…
In the face of mounting numerical evidence, Metlitski and Grover [arXiv:1112.5166] have given compelling analytical arguments that systems with spontaneous broken continuous symmetry contain a sub-leading contribution to the entanglement…
We construct a natural invariant measure concentrated on the set of square-free numbers, and invariant under the shift. We prove that the corresponding dynamical system is isomorphic to a translation on a compact, Abelian group. This…
We introduce an information-theoretic framework for smooth structures on topological manifolds, replacing coordinate charts with small-scale entropy data of local probability probes. A concise set of axioms identifies admissible coordinate…
A Bernoulli factory is an algorithmic procedure for exact sampling of certain random variables having only Bernoulli access to their parameters. Bernoulli access to a parameter $p \in [0,1]$ means the algorithm does not know $p$, but has…
Sinai proved that a nonatomic ergodic measure-preserving system has any Bernoulli shift of no greater entropy as a factor. Given a Bernoulli shift, we show that any other Bernoulli shift that is of strictly less entropy and is…
We consider zero-temperature, stochastic Ising models with nearest-neighbor interactions and an initial spin configuration chosen from a symmetric Bernoulli distribution (corresponding physically to a deep quench). Whether a final state…
In this paper, we study the problem of control of discrete-time nonlinear systems in Lure form over erasure channels at the input and output. The input and output channel uncertainties are modeled as Bernoulli random variables. The main…
We consider an independent and identically distributed (i.i.d.) random dynamical system of simple linear transformations on the unit interval $T_{\beta}(x)=\beta x$ (mod $1$), $x\in[0,1]$, $\beta>0$, which are the so-called…
Entropy dimension is an entropy-type quantity which takes values in $[0,1]$ and classifies different levels of intermediate growth rate of complexity for dynamical systems. In this paper, we consider the complexity of skew products of…
We are interested to the multifractal analysis of inhomogeneous Bernoulli products which are also known as coin tossing measures. We give conditions ensuring the validity of the multifractal formalism for such measures. On another hand, we…
We are interested to the multifractal analysis of inhomogeneous Bernoulli products which are also known as coin tossing measures. We give conditions ensuring the validity of the multifractal formalism for such measures. On another hand, we…
Let $G$ be a connected semisimple Lie group with finite centre, and let $M= \Gamma \backslash G$ be a compact homogeneous manifold. Under a spectral gap assumption, we show that smooth time-changes of any unipotent flow on $M$ have…
We consider a random dynamical system obtained by switching between the flows generated by two smooth vector fields on the 2d-torus, with the random switchings happening according to a Poisson process. Assuming that the driving vector…
Polydisperse systems are commonly encountered when dealing with soft matter in general or any non simple fluid. Yet their treatment within the framework of statistical thermodynamics is a delicate task as the latter has been essentially…
In this note we give examples of Hamiltonian diffeomorphisms which are on one hand dynamically complicated, for instance with positive topological entropy, and on the other hand minimal from the perspective of Floer theory. The minimality…
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 construct two staircase rank one transformations whose Cartesian product is not loosely Bernoulli.