Related papers: Exponential Decay of Lebesgue Numbers
We construct model sets arising from cut and project schemes in Euclidean spaces whose associated Delone dynamical systems have positive toplogical entropy. The construction works both with windows that are proper and with windows that have…
The notion of metric entropy dimension is introduced to measure the complexity of entropy zero dynamical systems. For measure preserving systems, we define entropy dimension via the dimension of entropy generating sequences. This…
In this paper, we generalize a recently obtained result by Kopaliani and Zviadadze from the one-variable case to the several-variable case. Specifically, in terms of decreasing rearrangement, we characterize those exponents $p(\cdot)$ for…
The tilings of lozenges in 2 dimensions and of rhomboedra in 3 dimensions are studied when they are constrained by fixed boundary conditions. We establish a link between those conditions and free or periodic boundary ones: the entropy is…
We show the existence of large $\mathcal C^1$ open sets of area preserving endomorphisms of the two-torus which have no dominated splitting and are non-uniformly hyperbolic, meaning that Lebesgue almost every point has a positive and a…
We study entanglement dynamics in a diagonal dephasing model in which the strength of interaction decays exponentially with distance -- the so-called l-bit model of many-body localization. We calculate the exact expression for entanglement…
We present a new methodology for the characterization of the metric entropy of infinite-dimensional ellipsoids with exponentially decaying semi-axes. This procedure does not rely on the explicit construction of coverings or packings and…
Topological study of existing random simplicial complexes is non-trivial and has led to several seminal works. However, the applicability of such studies is limited since the randomness there is usually governed by a single parameter. With…
Final version. To appear in Discrete and Continuous Dynamical Systems - A.
The principle of entropy increase is not only the basis of statistical mechanics, but also closely related to the irreversibility of time, the origin of life, chaos and turbulence. In this paper, we first discuss the dynamic system…
We consider a random generalisation of the classical Fibonacci substitution. The substitution we consider is defined as the rule mapping $\mathtt{a}\mapsto \mathtt{baa}$ and $\mathtt{b} \mapsto \mathtt{ab}$ with probability $p$ and…
Given a monotone convex function on the space of essentially bounded random variables with the Lebesgue property (order continuity), we consider its extension preserving the Lebesgue property to as big solid vector space of random variables…
A power-free language is characterized by the number of symbols used and a limit on how many times a block of symbols can repeat consecutively. For certain values of these parameters, it is known that the number of legal words grows…
We give some natural sufficient conditions for balls in a metric space to have small intersection. Roughly speaking, this happens when the metric space is (i) expanding and (ii) well-spread, and (iii) a certain random variable on the…
We evaluate the entanglement entropy of exactly solvable Hamiltonians corresponding to general families of three-dimensional topological models. We show that the modification to the entropic area law due to three-dimensional topological…
Topological entropy is a common measure of the rate of mixing in a flow. It can be computed by partition methods, or by estimating the growth rate of material lines or other material elements. This requires detailed knowledge of the…
We show that the Gauss-Bonnet term can have physical effects in four dimensions. Specifically, the entropy of a black hole acquires a correction that is proportional to the Euler characteristic of the cross sections of the horizon. While…
We derive the porous medium equation from an interacting particle system which belongs to the family of exclusion processes, with nearest neighbor exchanges. The particles follow a degenerate dynamics, in the sense that the jump rates can…
We consider partially hyperbolic diffeomorphisms $f$ with a one-dimensional central direction such that the unstable entropy exceeds the stable entropy. Our main result proves that such maps have a finite number of ergodic measures of…
We study exponential decay of eigenfunctions of self-adjoint higher order elliptic operators on $\R^d$. We show that the possible critical decay rates are determined algebraically. In addition we show absence of super-exponentially decaying…