Related papers: Analyzing a Seneta's conjecture by using the Willi…

We present a method of generation of exact and explicit forms of one-sided, heavy-tailed Levy stable probability distributions g_{\alpha}(x), 0 \leq x < \infty, 0 < \alpha < 1. We demonstrate that the knowledge of one such a distribution…

We show a new functional limit theorem for weakly dependent regularly varying sequences of random vectors. As it turns out, the convergence takes place in the space of R^d valued c\`{a}dl\`{a}g functions endowed with the so-called weak M1…

The Swampland program relies heavily on the conjecture that there can only be a finite number of flux vacua (FFV conjecture). Stipulating this FFV conjecture and applying it to some older work in flux vacua construction we show that within…

Some limit theorems of the type $\int_{\Omega}f_n dm_n -- --> \int_{\Omega}f dm$ are presented for scalar, (vector), (multi)-valued sequences of m_n-integrable functions f_n. The convergences obtained, in the vector and multivalued…

This article is a study on the summability of random Fourier--Jacobi series of some functions in different spaces. We consider the random series $ \sum_{n=0}^\infty a_nA_n(\omega)p_n^{(\gamma,\delta)}(y), $ where…

In this paper functions $f:D\to\mathbb{R}$ satisfying the inequality \[ f\Big(\frac{x+y}{2}\Big)\leq\frac12f(x)+\frac12f(y) +\varphi\Big(\frac{x-y}{2}\Big) \qquad(x,y\in D) \] are studied, where $D$ is a nonempty convex subset of a real…

Let $f$ be a real arithmetic function and let $g:[1,\infty[\to{\mathbb R}$ be a smooth function. We describe two emblematic instances in which saddle-point estimates may be used to evaluate the frequency, on the set of integers $n\leqslant…

We consider a discrete-time branching random walk in the boundary case, where the associated random walk is in the domain of attraction of an $\alpha$-stable law with $1<\alpha<2$. We prove that the derivative martingale $D_n$ converges to…

We calculate some infinite sums containing the digamma function in closed-form. These sums are related either to the incomplete beta function or to the Bessel functions. The calculations yield interesting new results as by-products, such as…

We prove that vertex-reinforced random walk on the integers with weight of order k to the power alpha, for alpha in [0, 1/2), is recurrent. This confirms a conjecture of Volkov for alpha<1/2. The conjecture for alpha in [1/2, 1) remains…

The aim of this paper is to propose an extension of the Wilf conjecture to semimodules over a numerical semigroup through a new approach toward the solution of the Wilf conjecture on numerical semigroups. The key point is the introduction…

Let $\Omega$ be a set of positive integers and let $f:\Omega \rightarrow \Omega$ be an arithmetic function. Let $V = (v_i)_{i=1}^n$ be a finite sequence of positive integers. An integer $m \in \Omega$ has \textit{increasing-decreasing…

The purpose of this paper is to study a generalization of strongly $\eta$-convex functions using the fractal calculus developed by Yang \cite{Yang}, namely generalized strongly $\eta$-convex function. Among other results, we obtain some…

We provide a generalization of Theorem 1 in Bartkiewicz, Jakubowski, Mikosch and Wintenberger (2011) in the sense that we give sufficient conditions for weak convergence of finite dimensional distributions of the partial sum processes of a…

The Fourier-Entropy Influence (FEI) Conjecture states that for any Boolean function $f:\{+1,-1\}^n \to \{+1,-1\}$, the Fourier entropy of $f$ is at most its influence up to a universal constant factor. While the FEI conjecture has been…

We define a switch function to be a function from an interval to $\{1,-1\}$ with a finite number of sign changes. (Special cases are the Walsh functions.) By a topological argument, we prove that, given $n$ real-valued functions, $f_1,…

In this article we study some properties of the discrete convolution of Liouville function $S(n):=\sum_{m_{1}+m_{2}=n}\lambda\left(m_{1}\right)\lambda\left(m_{2}\right)$, which is a Goldbach-type counting function of representations. In…

Motivated by applications to prediction and forecasting, we suggest methods for approximating the conditional distribution function of a random variable Y given a dependent random d-vector X. The idea is to estimate not the distribution of…

The symmetric function theorem states that a polynomial that is invariant under permutation of variables, is a polynomial in the elementary symmetric polynomials. We deduce this classical result, in the analytic setting, from the…

Inspired by recent work of A. Mardani which elaborates on the elementary fact that for any continuous function $f:\omega_1\times\mathbb{R}\to\mathbb{R}$, there is an $\alpha\in\omega_1$ such that $f(\langle\beta,x\rangle) =…