Related papers: Averages along cubes for not necessarily commuting…

Associated to any finite metric space are a large number of objects and quantities which provide some degree of structural or geometric information about the space. In this paper we show that in the setting of subsets of weighted Hamming…

We define a uniformly behaved in ${\mathbb N}$ arithmetic sequence ${\bf a}$ and an ${\bf a}$-mean Lyapunov stable dynamical system $f$. We consider the time-average of a continuous function $\phi$ along the ${\bf a}$-orbit of $f$ up to…

Properties of weighted averages are studied for the general case that the individual measurements are subject to hidden correlations and have asymmetric statistical as well as systematic errors. Explicit expressions are derived for an…

We unify and extend some previous results about cubic ergodic averages and sets of positive density in products of groups. This provides a joint generalization of earlier work of the author in the case of two commuting actions of an…

We analyze the question whether sliding window time averages applied to stationary increment processes converge to a limit in probability. The question centers on averages, correlations, and densities constructed via time averages of the…

Convergence properties of random ergodic averages have been extensively studied in the literature. In these notes, we exploit a uniform estimate by Cohen \& Cuny who showed convergence of a series along randomly perturbed times for…

The well-known Jewett-Krieger's Theorem states that each ergodic system has a strictly ergodic model. Strengthening the model by requiring that it is strictly ergodic under some group actions, and building the connection of the new model…

We confirm a conjecture posed by Bergelson, Moreira, and Richter (arXiv:1711.05729), and in particular show that for every probability measure preserving system $(X,\mathscr{B},\mu,T)$, every $k\in \mathbb{N}$, every set $A\in \mathscr{B}$…

We obtain new results pertaining to convergence and recurrence of multiple ergodic averages along functions from a Hardy field. Among other things, we confirm some of the conjectures posed by Frantzikinakis in [Fra10; Fra16] and obtain…

Certain notions of convergence of sequences functions such as pointwise convergence and (uniform) convergence on compact or bounded sets come from suitable topological function spaces; see [1]. Under certain conditions these topologies…

A generalized definition of average, termed the q-average, is widely employed in the field of nonextensive statistical mechanics. Recently, it has however been pointed out that such an average value may behave unphysical under specific…

This paper studies homothetic and more general weighted averages for flows. Absolutely continuous convolutions of singular weights are considered, thereby strengthening Kozlov-Treshchev's result on nonuniform averages for ergodic flows. The…

Geodesic metric spaces support a variety of averaging constructions for given finite sets. Computing such averages has generated extensive interest in diverse disciplines. Here we consider the inverse problem of recognizing computationally…

In this paper, we reduce pointwise convergence of polynomial ergodic averages of general measure-preserving system acted by $\mathbb{Z}^{d}$ to the case of measure-preserving system acted by $\mathbb{Z}^{d}$ with zero entropy. As an…

This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary…

We examine Fourier frames and, more generally, frame measures for different probability measures. We prove that if a measure has an associated frame measure, then it must have a certain uniformity in the sense that the weight is distributed…

We will show that the sequences appearing in Bourgain's double recurrence result are good universal weights to the multiple recurrence averages with commuting measure-preserving transformations in norm. This will extend the pointwise…

Quantum measurements are noncontextual, with outcomes independent of which other commuting observables are measured at the same time, when consistently analyzed using principles of Hilbert space quantum mechanics rather than classical…

Based on T.Tao's result of norm convergence of multiple ergodic averages for commut-ing transformation, we obtain there is a subsequence which converges almost everywhere. Meanwhile, the ergodic behaviour, which the time average is equal to…

Let $G = (V,E)$ be a connected graph. A probability measure $\mu$ on $V$ is called "balanced" if it has the following property: if $T_\mu(v)$ denotes the "earth mover's" cost of transporting all the mass of $\mu$ from all over the graph to…