Related papers: On Inhomogeneous Poissonian Pair Correlations
A sequence $(x_n)$ on the torus is said to have Poissonian pair correlations if $\# \{1\le i\neq j\le N: |x_i-x_j| \le s/N\}=2sN(1+o(1))$ for all reals $s>0$, as $N\to \infty$. It is known that, if $(x_n)$ has Poissonian pair correlations,…
In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation…
This study presents an abelian group approach to analyzing inconsistency in pairwise comparisons. However, it wrongly assumes that an inconsistency indicator can take values in any abelian linearly ordered group. The followup publication…
We study an extension of Montgomery's pair-correlation conjecture and its relevance in some problems on the distribution of prime numbers.
We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional…
In the first part we associate a periodic sequence to a partition and study the connection the distribution of elements of uniform limit of the sequences. Then some facts of statistical independence of these limits are proved
Non-linear maps can possess various dynamical behaviors varying from stable steady states and cycles to chaotic oscillations. Most models assume that individuals within a given population are identical ignoring the fundamental role of…
Recent attempts to determine the pion polarizability by dispersion relations yield values that disagree with the predictions of chiral perturbation theory. These dispersion relations are based on specific forms for the absorptive part of…
It is shown that short-range correlations between large prime numbers (~10^5 and larger) have a Poissonian nature. Correlation length \zeta = 4.5 for the primes ~10^5 and it is increasing logarithmically according to the prime number…
In this paper we extend the well-known investigations of Montgomery and Goldston & Montgomery, concerning the pair-correlation function and its relations with the distribution of primes in short intervals, to a more general version of the…
Approximate expressions for correlation functions in binary inhomogeneous mixtures are derived in a framework of the mesoscopic theory [Ciach A., Mol. Phys., 2011, {\textbf{109}}, 1101]. Fluctuation contribution is taken into account in a…
Studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the distribution of particles at `microscales' to predict physical properties at `macroscales', whether for a liquid, composite material, or…
The pair correlation is a localized statistic for sequences in the unit interval. Pseudo-random behavior with respect to this statistic is called Poissonian behavior. The metric theory of pair correlations of sequences of the form $(a_n…
We suggest a homotopical description of the Poisson bracket invariants for tuples of closed sets in symplectic manifolds. It implies that these invariants depend only on the union of the sets along with topological data.
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 analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson…
The inhomogeneous metric theory for the set of simultaneously $\psi$-approximable points lying on a planar curve is developed. Our results naturally incorporate the homogeneous Khintchine-Jarnik type theorems recently established in [Ann.…
Commonalities and differences in correlation analysis in terms of phase space, conditioning and uncorrelatedness are discussed. The Poisson process is not generally appropriate as reference distribution for normalisation and cumulants, so…
This paper shows that one needs to be careful when making statements on potential links between correlation and coskewness. Specifically, we first show that, on the one hand, it is possible to observe any possible values of coskewness among…
What constitutes jointly Poisson processes remains an unresolved issue. This report reviews the current state of the theory and indicates how the accepted but unproven model equals that resulting from the small time-interval limit of…