Related papers: Remarks about inhomogeneous pair correlations

We prove that analogues of the Hardy-Littlewood generalised twin prime conjecture for almost primes hold on average. Our main theorem establishes an asymptotic formula for the number of integers $n=p_1p_2 \leq X$ such that $n+h$ is a…

We discuss the relationship between ratio asymptotics for general orthogonal polynomials and the asymptotics of the associated Bergman shift operator. More specifically, we consider the case in which a measure is supported on an infinite…

We consider covariance asymptotics for linear statistics of general stationary random measures in terms of their truncated pair correlation measure. We give exact infinite series-expansion formulas for covariance of smooth statistics of…

We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…

Association models for a pair of random elements $X$ and $Y$ (e.g., vectors) are considered which specify the odds ratio function up to an unknown parameter $\bolds\theta$. These models are shown to be semiparametric in the sense that they…

We study an extension of Montgomery's pair-correlation conjecture and its relevance in some problems on the distribution of prime numbers.

Let $X$ be an $n$-element set. A set-pair system $\mbox{$\cal P$}=\{(A_i,B_i)\}_{1\leq i\leq m}$ is a collection of pairs of disjoint subsets of $X$. It is called skew Bollob\'as system if $A_i\cap B_j\neq \emptyset$ for all $1\leq i<j \leq…

We propose new summary statistics to quantify the association between the components in coverage-reweighted moment stationary multivariate random sets and measures. They are defined in terms of the coverage-reweighted cumulant densities and…

Pairwise comparison matrices are increasingly used in settings where some pairs are missing. However, there exist few inconsistency indices for similar incomplete data sets and no reasonable measure has an associated threshold. This paper…

We investigate additive properties of sets $A,$ where $A=\{a_1,a_2,\ldots ,a_k\}$ is a monotone increasing set of real numbers, and the differences of consecutive elements are all distinct. It is known that $|A+B|\geq c|A||B|^{1/2}$ for any…

Meta-analyses are commonly performed based on random-effects models, while in certain cases one might also argue in favour of a common-effect model. One such case may be given by the example of two "study twins" that are performed according…

We discuss quantum correlations in systems of indistinguishable particles in relation to entanglement in composite quantum systems consisting of well separated subsystems. Our studies are motivated by recent experiments and theoretical…

We characterize the growth of the Sibson and Arimoto mutual informations and $\alpha$-maximal leakage, of any order that is at least unity, between a random variable and a growing set of noisy, conditionally independent and…

The symbol error rate of the minimum distance detector for an arbitrary multi-dimensional constellation impaired by additive white Gaussian noise is characterized as the product of a completely monotone function with a non-negative power of…

Extensions of nuclear supersymmetry are discussed, together with a proposal for new, more stringent and precise tests that probe the susy classification and specific two-particle correlations among supersymmetric partners. The combination…

We consider the problem of hypotheses testing with the basic simple hypothesis: observed sequence of points corresponds to stationary Poisson process with known intensity against a composite one-sided parametric alternative that this is a…

We study a 2-parametric family of probability measures on an infinite-dimensional simplex (the Thoma simplex). These measures originate in harmonic analysis on the infinite symmetric group (S.Kerov, G.Olshanski and A.Vershik, Comptes Rendus…

We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…

It is sometimes desirable in choiceless constructions of set theory that one iteratively extends some ground model without adding new sets of ordinals after the first extension. Pushing this further, one may wish to have models $V \subseteq…

We consider the asymptotics of the correlation functions of the characteristic polynomials of the hermitian Wigner matrices $H_n=n^{-1/2}W_n$. We show that for the correlation function of any even order the asymptotic coincides with this…