Related papers: Sensitivity and Devaney's chaos in uniform spaces

We prove a concentration inequality for invariant means on topological groups, namely for such adapted to a chain of amenable topological subgroups. The result is based on an application of Azuma's martingale inequality and provides a…

A short proof is given of a necessary and sufficient condition for the normalized occupation measure of a L\'evy process in a metrizable compact group to be asymptotically uniform with probability one.

We compute explicit bounds in the normal and chi-square approximations of multilinear homogenous sums (of arbitrary order) of general centered independent random variables with unit variance. In particular, we show that chaotic random…

We investigate unitarisability of groups by looking at actions on the cone of positive invertible operators of a Hilbert space. This way, we give a geometric prove to a result by Gilles Pisier on the existence of some universal constants…

We define and study stronger forms of Devaney chaos and name it as $\mathscr{F}-$Devaney chaos, where $\mathscr{F}$ is a family of subsets of $\mathbb{N}$. Examples of maps which is $\mathscr{F}_t-$Devaney chaotic but not…

We examine the sensitivity of wavefunction intensities in chaotic quantum systems to small changes in an arbitrary external perturbation. A universal scaling is proposed for all three Dyson ensembles and a novel theoretical approach is used…

We present several new phenomena about almost sure convergence on homogeneous chaoses that include Gaussian Wiener chaos and homogeneous sums in independent random variables. Concretely, we establish the fact that almost sure convergence on…

We describe conditions that characterize amenability for groups in terms of positive definite functions valued in a von Neumann algebra.

In this paper, we apply Devroye inequality to study various statistical estimators and fluctuations of observables for processes. Most of these observables are suggested by dynamical systems. These applications concern the co-variance…

We prove that for certain actions of a discrete countable residually finite amenable group acting on a compact metric space with specification property, periodic measures are dense in the set of invariant measures.

We generalize the notion of isoperimetric profiles of finitely generated groups to their actions by measuring the boundary of finite subgraphings of the orbit graphing. We prove that like the classical isoperimetric profiles for groups,…

We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…

In the setting of dominated statistical models, we provide conditions yielding strong continuity of the posterior distribution with respect to the observed data. We show some applications, with special focus on exponential models.

In this note, we give several equivalent definitions of Devaney's chaos

We show that materials made of scatterers distributed on a stealth hyperuniform point pattern can be transparent at densities for which an uncorrelated disordered material would be opaque due to multiple scattering. The conditions for…

Suppose a spacetime $M$ is a quotient of a spacetime $V$ by a discrete group of isometries. It is shown how causality conditions in the two spacetimes are related, and how can one learn about the future causal boundary on $M$ by studying…

We show that the universal minimimal proximal flow and the universal minimal strongly proximal flow of a discrete group can be realized as the Stone spaces of translation invariant Boolean algebras of subsets of the group satisfying a…

We survey results from amenability theory with an emphasis on applications to harmonic analysis on direct-limit groups.

We give upper and lower bounds of perturbation series for transition densities, corresponding to additive gradient perturbations satisfying certain space-time integrability conditions.

In this paper, we study discrete spectrum of invariant measures for countable discrete amenable group actions. We show that an invariant measure has discrete spectrum if and only if it has bounded measure complexity. We also prove that,…