Related papers: On Pair Correlation of Sequences
We review recent experimental results on intermittency and multidimensional particle correlations in high-energy leptonic, hadronic and nuclear collisions. We discuss different theoretical models, including self-similar cascading and QCD…
We study certain polyadicly continuous sequences from point of view the probability theory.
Pseudorandom sequences are used extensively in communications and remote sensing. Correlation provides one measure of pseudorandomness, and low correlation is an important factor determining the performance of digital sequences in…
The notion of "paired" fermions is central to important condensed matter phenomena such as superconductivity and superfluidity. While the concept is widely used and its physical meaning is clear there exists no systematic and mathematical…
Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to raise and recall awareness of some of these limitations by…
Particle pair-correlations are broadly used to describe particle distributions in chemistry, physics, and material science. Many theoretical methods require the pair-correlation to predict material properties such as fluid flow, thermal…
We prove that any increasing sequence of real numbers with average gap $1$ and Poisson pair correlations has some gap that is at least $3/2+10^{-9}$. This improves upon a result of Aistleitner, Blomer, and Radziwill.
We study an extension of Montgomery's pair-correlation conjecture and its relevance in some problems on the distribution of prime numbers.
We show that any sequence $(x_n)_{n \in \mathbb{N}} \subseteq [0,1]$ that has Poissonian correlations of $k$-th order is uniformly distributed, also providing a quantitative description of this phenomenon. Additionally, we extend…
We consider finite Bernoulli convolutions with a parameter $1/2 < r < 1$ supported on a discrete point set, generically of size $2^N$. These sequences are uniformly distributed with respect to the infinite Bernoulli convolution measure…
We establish new pair correlation results for certain generic homogenous diagonal forms evaluated on the integers. Methods are analytic leading to explicit quantitative statements.
In this paper we introduce the notion of the $P$-sequences and apply their properties in studying representability of real numbers. Another application of $P$-sequences we find in generating the Prouhet-Tarry-Escott pairs.
Many applications benefit from theory relevant to the identification of variables having large correlations or partial correlations in high dimension. Recently there has been progress in the ultra-high dimensional setting when the sample…
We study the statistics of pairs from the sequence $(n^\alpha)_{n\in\mathbb{N}^*}$, for every parameter $\alpha \in \, ]0,1[$. We prove the convergence of the empirical pair correlation measures towards a measure with an explicit density.…
The paper is a survey of notions and results related to classical and new generalizations of the notion of a periodic sequence. The topics related to almost periodicity in combinatorics on words, symbolic dynamics, expressibility in logical…
The Poisson probability distribution is frequently encountered in physical science measurements. In spite of the simplicity and familiarity of this distribution, there is considerable confusion among physicists concerning the description of…
In this work we describe and compare the classic inner product and Pearson correlation coefficient as well as the recently introduced real-valued Jaccard and coincidence indices. Special attention is given to diverse schemes for taking into…
Pearson's correlation is one of the most common measures of linear dependence. Recently, Bernardo (2015) introduced a flexible class of priors to study this measure in a Bayesian setting. For this large class of priors we show that the…
We review recent theoretical developments in understanding the intermittency phenomenon observed in high-energy leptonic, hadronic and nuclear collisions. In particular, we discuss self-similar cascading and QCD parton showers, models with…
In this short note, we reformulate the task of calculating the pair correlation statistics of a Kronecker sequence as a lattice point counting problem. This can be done analogously to the lattice based approach which was used to (re-)prove…