Related papers: Correlations of values of random diagonal forms

We consider bond percolation on random graphs with given degrees and bounded average degree. In particular, we consider the order of the largest component after the random deletion of the edges of such a random graph. We give a rough…

Let $X_1, X_2,\ldots, X_n$ be $n$ independent and identically distributed random variables, here $n \geq 2.$ Let $X_{(1)}, X_{(2)}, \ldots, X_{(n)}$ be the order statistics of $X_1, X_2,..., X_n.$ In this note we proved that: (I) If $X_1,…

There are given characterizations of the exponential distribution by the properties of the independence of linear forms with random coefficients. Related results based on the constancy of regression of one statistic on a linear form are…

Composite likelihood usually ignores dependencies among response components, while variational approximation to likelihood ignores dependencies among parameter components. We derive a Gaussian variational approximation to the composite…

We study visibility inside the vacant set of three models in $\mathbb R^d$ with slow decay of spatial correlations: Brownian interlacements, Poisson cylinders and Boolean model. For each of them, we obtain sharp asymptotic bounds on the…

Consider an independent site percolation model on $\Z^d,\ d\geq 2$, with parameter $p \in (0,1)$, where there are only nearest neighbor bonds and long range bonds of length $k$ parallel to some coordinate axis. We show that the percolation…

We study the distribution of spacings between the fractional parts of $n^d\alpha$. For $\alpha$ of high enough Diophantine type we prove a necessary and sufficient condition for $n^d\alpha\mod 1, 1\leq n\leq N,$ to be Poissonian as $N\to…

Measuring the correlation (association) between two random variables is one of the important goals in statistical applications. In the literature, the covariance between two random variables is a widely used criterion in measuring the…

The influence of pure statistical fluctuations on $K/\pi$ ratio is investigated in an event-by-event way. Poisson and the modified negative binomial distributions are used as the multiplicity distributions since they both have statistical…

We consider large complex random sample covariance matrices obtained from "spiked populations", that is when the true covariance matrix is diagonal with all but finitely many eigenvalues equal to one. We investigate the limiting behavior of…

The Gaussian correlation inequality for multivariate zero-mean normal probabilities of symmetrical n-rectangles can be considered as an inequality for multivariate gamma distributions (in the sense of Krishnamoorthy and Parthasarathy [5])…

For an integer $k\geq 2$, let $\{F^{(k)}_{n}\}_{n\geqslant 2-k}$ be the $ k$--generalized Fibonacci sequence which starts with $0, \ldots, 0,1$ (a total of $k$ terms) and for which each term afterwards is the sum of the $k$ preceding terms.…

We introduce, and analyze, three measures for degree-degree dependencies, also called degree assortativity, in directed random graphs, based on Spearman's rho and Kendall's tau. We proof statistical consistency of these measures in general…

Poisson transversals are those submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In a previous note we proved a normal form theorem around such submanifolds. In this communication, we…

We consider $p$-orientations, which are defined to be orientations of $d$-regular graphs such that every vertex either has in-degree $p$ or out-degree $p$. These generalise the orientations considered in Jaeger's conjecture, where $d=4p+1$.…

In this paper we study Appell polynomials by connecting them to random variables. This probabilistic approach yields, e.g., the mean value property which is fundamental in the sense that many other properties can be derived from it. We also…

We develop a comprehensive analysis of the Kirkwood-Dirac distributions in classical optics, revealing their deep connection with optical coherence as fundamental concept in optics. From their very definition, the Kirkwood-Dirac…

Let X be a smooth algebraic variety over a field K containing the real numbers. We introduce the notion of twisted associative (resp. Poisson) deformation of the structure sheaf of X. These are stack-like versions of usual deformations. We…

Permutations of correlated sequences of random variables appear naturally in a variety of applications such as graph matching and asynchronous communications. In this paper, the asymptotic statistical behavior of such permuted sequences is…

The curse of dimensionality is a common phenomenon which affects analysis of datasets characterized by large numbers of variables associated with each point. Problematic scenarios of this type frequently arise in classification algorithms…