Related papers: A p-adic Poissonian Pair Correlation Concept
The Particle Number Projected Generator Coordinate Method is formulated for the pairing Hamiltonian in a detailed way in the projection after variation and the variation after projection methods. The dependence of the wave functions on the…
Continued fractions have a long history in number theory, especially in the area of Diophantine approximation. The aim of this expository paper is to survey the main results on the theory of $p$--adic continued fractions, i.e. continued…
We obtain quenched hitting distributions to be compound Poissonian for a certain class of random dynamical systems. The theory is general and designed to accommodate non-uniformly expanding behavior and targets that do not overlap much with…
Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the…
The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical…
We study the notion of dp-minimality, beginning by providing several essential facts, establishing several equivalent definitions, and comparing dp-minimality to other minimality notions. The rest of the paper is dedicated to examples. We…
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 consider the Rosenzweig-Porter model of random matrix which interpolates between Poisson and gaussian unitary statistics and compute exactly the two-point correlation function. Asymptotic formulas for this function are given near the…
We establish new pair correlation results for certain generic homogenous diagonal forms evaluated on the integers. Methods are analytic leading to explicit quantitative statements.
This paper is concerned with inference in the linear model with dyadic data. Dyadic data is data that is indexed by pairs of "units", for example trade data between pairs of countries. Because of the potential for observations with a unit…
This paper introduces a causation coefficient which is defined in terms of probabilistic causal models. This coefficient is suggested as the natural causal analogue of the Pearson correlation coefficient and permits comparing causation and…
Directed acyclic graphs are widely used to describe the causal effects among random variables, and the inference of those causal effects has become an popular topic in statistics and machine learning, and has wide applications in…
The statistically unbounded $p$-convergence is an abstraction of the statistical order, unbounded order, and $p$-convergences. We investigate the concept of the statistically unbounded convergence on lattice-normed Riesz spaces with respect…
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…
In this short paper I consider relation between measurements, numbers and p-adic mathematical physics. p-Adic numbers are not result of measurements, but nevertheless they play significant role in description of some systems and phenomena.…
The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
Canonical correlation analysis is a family of multivariate statistical methods for the analysis of paired sets of variables. Since its proposition, canonical correlation analysis has for instance been extended to extract relations between…
The distortion of the regular motion in a quantum system by its coupling to the continuum of decay channels is investigated. The regular motion is described by means of a Poissonian ensemble. We focus on the case of only few channels K<10.…
Overrepresentation of bidirectional connections in local cortical networks has been repeatedly reported and is in the focus of the ongoing discussion of non-random connectivity. Here we show in a brief mathematical analysis that in a…