Related papers: An Equidistribution Result for Differences Associa…
The aim of this paper is to present new upper bounds for the distance between a properly normalized permanent of a rectangular complex matrix and the product of the arithmetic means of the entries of its columns. It turns out that the…
This is a companion paper to arXiv:2312.10772. We deduce an equidistribution theorem for periodic nilsequences and use this theorem to give two applications in arithmetic combinatorics. The first application is quasi-polynomial bounds for a…
Non-uniform estimates are obtained for Poisson, compound Poisson, translated Poisson, negative binomial and binomial approximations to sums of of m-dependent integer-valued random variables. Estimates for Wasserstein metric also follow…
We elaborate the notions of Martin-L\"of and Schnorr randomness for real numbers in terms of uniform distribution of sequences. We give a necessary condition for a real number to be Schnorr random expressed in terms of classical uniform…
We give sharp, uniform estimates for the probability that the empirical distribution function for n uniform-[0,1] random variables stays to one side of a given line.
We derive upper and lower bounds on the sum of distances of a spherical code of size $N$ in $n$ dimensions when $N\sim n^\alpha, 0<\alpha\le 2.$ The bounds are derived by specializing recent general, universal bounds on energy of spherical…
We compute the second and third levels of the Lasserre hierarchy for the spherical finite distance problem. A connection is used between invariants in representations of the orthogonal group and representations of the general linear group,…
The rate of convergence of the distribution of the length of the longest increasing subsequence, toward the maximal eigenvalue of certain matrix ensembles, is investigated. For finite-alphabet uniform and nonuniform i.i.d. sources, a rate…
The Tribonacci sequence $\mathbb{T}$ is the fixed point of the substitution $\sigma(a,b,c)=(ab,ac,a)$. In this note, we get the explicit expressions of all squares, and then establish the tree structure of the positions of repeated squares…
We study equidistribution properties of nil-orbits $(b^nx)_{n\in\N}$ when the parameter $n$ is restricted to the range of some sparse sequence that is not necessarily polynomial. For example, we show that if $X=G/\Gamma$ is a nilmanifold,…
The discrete distribution of the length of longest increasing subsequences in random permutations of $n$ integers is deeply related to random matrix theory. In a seminal work, Baik, Deift and Johansson provided an asymptotics in terms of…
Uniform convergence of empirical norms - empirical measures of squared functions - is a topic which has received considerable attention in the literature on empirical processes. The results are relevant as empirical norms occur due to…
In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying…
It is shown that each continuous transformation $h$ from Euclidean $m$-space ($m>1$) into Euclidean $n$-space that preserves the equality of distances (that is, fulfils the implication $|x-y|=|z-w|\Rightarrow|h(x)-h(y)|=|h(z)-h(w)|$) is a…
In a previous paper with the same title, we gave an upper bound for the exponent of uniform rational approximation to a quadruple of $\mathbb{Q}$-linearly independent real numbers in geometric progression. Here, we explain why this upper…
The predictability of a sequence is defined as the asymptotic performance of the best performing predictor in a given class. The value of the predictability of a sequence will in general depend on the choice of this predictor class. The…
Let $S$ be a set of $n$ weighted points in the plane and let $R$ be a query range in the plane. In the range closest pair problem, we want to report the closest pair in the set $R \cap S$. In the range minimum weight problem, we want to…
We find the closest approximation to 1 from below using a sum of $n$ Egyptian fractions.
In this paper, a new measurement to compare two large-scale graphs based on the theory of quantum probability is proposed. An explicit form for the spectral distribution of the corresponding adjacency matrix of a graph is established. Our…
Several properties of stationary subdivision schemes are nowadays well understood. In particular, it is known that the polynomial generation and reproduction capability of a stationary subdivision scheme is strongly connected with sum…