Related papers: The distribution of vector-valued Rademacher serie…
The parton distribution functions determined by CTEQ at low $Q^2$ are used as inputs to test the validity of the valon model. The valon distributions in a nucleon are first found to be nearly $Q$ independent. The parton distribution in a…
Let $\Delta_{k;n}$ be the maximum number of common neighbors of a set of $k$ vertices in $G(n,p)$. In this paper, we find $a_n$ and $\sigma_n$ such that $\frac{\Delta_{k;n}-a_n}{\sigma_n}$ converges in distribution to a random variable…
We apply L.~Schwartz' theory of vector valued distributions in order to simplify, unify and generalize statements about convolvability of distributions, their regularization properties and topological properties of sets of distributions.…
Symbolic Data Analysis works with variables for which each unit or class of units takes a finite set of values/categories, an interval or a distribution (an histogram, for instance). When to each observation corresponds an empirical…
We introduce the problem of transporting vector-valued distributions. In this, a salient feature is that mass may flow between vectorial entries as well as across space (discrete or continuous). The theory relies on a first step taken to…
Universality properties of the distribution of the generalized eigenvalues of a pencil of random Hankel matrices, arising in the solution of the exponential interpolation problem of a complex discrete stationary process, are proved under…
There is a natural pluripotential-theoretic extremal function V_{K,Q} associated to a closed subset K of C^m and a real-valued, continuous function Q on K. We define random polynomials H_n whose coefficients with respect to a related…
The problem of extrapolating the series in powers of small variables to the region of large variables is addressed. Such a problem is typical of quantum theory and statistical physics. A method of extrapolation is developed based on…
In this paper, we introduce a certain random variable closely related to the value-distribution of the Hurwitz zeta-function with algebraic parameter. We prove a version of the limit theorem, where the limit measure is presented by the law…
The dispersion of a diffusive scalar in a fluid flowing through a network has many applications including to biological flows, porous media, water supply and urban pollution. Motivated by this, we develop a large-deviation theory that…
Quantitative multivariate central limit theorems for general functionals of possibly non-symmetric and non-homogeneous infinite Rademacher sequences are proved by combining discrete Malliavin calculus with the smart path method for normal…
We consider propagation of optical pulses under the interplay of dispersion and Kerr non-linearity in optical fibres with impurities distributed at random uniformly on the fibre. By using a model based on the non-linear Schrodinger equation…
This note analyzes properties of the median $\nu$ of the Poisson distribution of order $k$. Given a value for the median in the interval $\nu\in[1,k]$, an equation to calculate the corresponding value of the rate parameter $\lambda$ is…
For any continuous zero-mean random variable (r.v.) X, a reciprocating function r is constructed, based only on the distribution of X, such that the conditional distribution of X given the (at-most-)two-point set {X,r(X)} is the zero-mean…
We show that, for sufficiently large integers $m$ and $X$, for almost all $a =1, ..., m$ the ratios $a/x$ and the products $ax$, where $|x|\le X$, are very uniformly distributed in the residue ring modulo $m$. This extends some recent…
In this paper, we study the distribution of the sequence of integers $d(n^2)$ under the assumption of the strong Riemann hypothesis. Under this assumption, we provide a refined asymptotic formula for the sum $\displaystyle\sum_{n\leq…
We study the discrepancy between the distribution of a vector-valued functional of i.i.d. random elements and that of a Gaussian vector. Our main contribution is an explicit bound on the convex distance between the two distributions,…
A finite form of de Finetti's representation theorem is established using elementary information-theoretic tools: The distribution of the first $k$ random variables in an exchangeable binary vector of length $n\geq k$ is close to a mixture…
The one-dimensional Dickman distribution arises in various stochastic models across number theory, combinatorics, physics, and biology. Recently, a definition of the multidimensional Dickman distribution has appeared in the literature,…
Let $f=(f_1,\ldots,f_n)$ be a system of $n$ complex homogeneous polynomials in $n$ variables of degree $d$. We call $\lambda\in\mathbb{C}$ an eigenvalue of $f$ if there exists $v\in\mathbb{C}^n\backslash\{0\}$ with $f(v)=\lambda v$,…