Related papers: Random series of functions and applications

We describe a curious dynamical system that results in sequences of real numbers in $[0,1]$ with seemingly remarkable properties. Let the function $f:\mathbb{T} \rightarrow \mathbb{R}$ satisfy $\hat{f}(k) \geq c|k|^{-2}$ and define a…

Inspired by Menshov's representation theorem, we prove that there exists a sequence of frequecies such that any measurable (complex valued) function on R can be represented as a sum of almost everywhere convergent trigonometric series with…

We consider reversible random walks in random environment obtained from symmetric long--range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and…

A classical fact of the theory of almost periodic functions is the existence of their asymptotic distributions. In probabilistic terms, this means that if $f$ is a Besicovitch almost periodic function and $V$ is a random variable uniformly…

Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…

We introduce a class of random graph processes, which we call flip processes. Each such process is given by a rule which is a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all labeled $k$-vertex graphs into itself ($k$…

Let $X,X_1,...,X_n$ be independent identically distributed random variables. The paper deals with the question about the behavior of the concentration function of the random variable $\sum_{k=1}^{n}a_k X_k$ according to the arithmetic…

A number of papers have examined various aspects of "random random" walks on finite groups; the purpose of this article is to provide a survey of this work and to show, bring together, and discuss some of the arguments and results in this…

We show that alpha stable L\'evy motions can be simulated by any ergodic and aperiodic probability preserving transformation. Namely we show: - for $0<\alpha<1$ and every $\alpha$ stable L\'evy motion $\mathbb{W}$, there exists a function f…

This paper has several major purposes. The central purpose is to describe the "Benford analysis" of a positive random variable and to summarize some results from investigations into base dependence of Benford random variables. The principal…

We present a class of multiplicative functions $f:\mathbb{N}\to\mathbb{C}$ with bounded partial sums. The novelty here is that our functions do not need to have modulus bounded by $1$. The key feature is that they pretend to be the constant…

Let $A$ be a subset of $\mathbb{Z} / N\mathbb{Z}$ and let $\mathcal{R}$ be the set of large Fourier coefficients of $A$. Properties of $\mathcal{R}$ have been studied in works of M.-- C. Chang, B. Green and the author. In the paper we…

Empirical processes for stationary, causal sequences are considered. We establish empirical central limit theorems for classes of indicators of left half lines, absolutely continuous functions and piecewise differentiable functions. Sample…

We derive and prove an explicit formula for the sum of the fractional parts of certain geometric series. Although the proof is straightforward, we have been unable to locate any reference to this result. This summation formula allows us to…

We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…

We consider the distribution of the polygonal paths joining partial sums of classical Kloosterman sums, as their parameter varies modulo a prime tending to infinity. Using independence of Kloosterman sheaves, we prove convergence in the…

Almost periodicity has been considered in Formal Language Theory in connection with some topics in Symbolic Dynamics. In (P\u{a}un and Marcus, Bulletin of EATCS 53 (1994)) some problems concerning this property are raised. For instance it…

We find conditions for stationary measures of random dynamical systems on surfaces having dissipative diffeomorphisms to be absolutely continuous. These conditions involve a uniformly expanding on average property in the future (UEF) and…

The article presents mathematical generalization of results which originated as solutions of practical problems, in particular, the modeling of transitional processes in electrical circuits and problems of resource allocation. However, the…

Periodicity is often studied in timeseries modelling with autoregressive methods but is less popular in the kernel literature, particularly for higher dimensional problems such as in textures, crystallography, and quantum mechanics. Large…