Related papers: On the generalized Kesten--McKay distributions
In earlier work, Billey--Konvalinka--Swanson studied the asymptotic distribution of the coefficients of Stanley's $q$-hook length formula, or equivalently the major index on standard tableaux of straight shape and certain skew shapes. We…
It is known that each symmetric stable distribution in $R^d$ is related to a norm on $R^d$ that makes $R^d$ embeddable in $L_p([0,1])$. In case of a multivariate Cauchy distribution the unit ball in this norm corresponds is the polar set to…
We prove Abelian and Tauberian theorems for regularised Cauchy transforms of positive Borel measures on the real line whose distribution functions grow at most polynomially at infinity. In particular, we relate the asymptotics of the…
We study statistical properties of Fourier coefficients of automorphic forms on GL(n). For most Hecke-Maass cusp forms, we give the asymptotic number of nonvanishing coefficients, show that there is a positive proportion of sign changes…
Computing the distribution of permanents of random matrices has been an outstanding open problem for several decades. In quantum computing, "anti-concentration" of this distribution is an unproven input for the proof of hardness of the task…
Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions are a special case where the density matrix is restricted to be diagonal. Density…
The bivariate Gaussian distribution has been a key model for many developments in statistics. However, many real-world phenomena generate data that follow asymmetric distributions, and consequently bivariate normal model is inappropriate in…
The generalized Poisson distribution is well known to be a compound Poisson distribution with Borel summands. As a generalization we present closed formulas for compound Bartlett and Delaporte distributions with Borel summands and a…
We introduce a novel family of projected distributions on the circle and the sphere, namely the circular and spherical projected Cauchy distributions, as promising alternatives for modelling circular and spherical data. The circular…
We propose point estimators for the three-parameter (location, scale, and the fractional parameter) variant distributions generated by a Wright function. We also provide uncertainty quantification procedures for the proposed point…
Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate…
For general thinning procedures, its inverse operation, the condensing, is studied and a link to integration-by-parts formulas is established. This extends the recent results on that link for independent thinnings of point processes to…
By a mixture density is meant a density of the form $\pi_{\mu}(\cdot)=\int\pi_{\theta}(\cdot)\times\mu(d\theta)$, where $(\pi_{\theta})_{\theta\in\Theta}$ is a family of probability densities and $\mu$ is a probability measure on $\Theta$.…
A duality formula, of the Hardy and Littlewood type for multidimensional Gaussian sums, is proved in order to estimate the asymptotic long time behavior of distribution of Birkhoff sums $S_n$ of a sequence generated by a skew product…
We compute the pion quark Generalised Parton Distribution H and quark Double Distributions in a coupled Bethe-Salpeter and Dyson-Schwinger approach in terms of quark flavors or isospin states. We use analytic expressions inspired by the…
We consider Kemp's q-analogue of the binomial distribution. Several convergence results involving the classical binomial, the Heine, the discrete normal, and the Poisson distribution are established. Some of them are q-analogues of…
We construct symmetric representations of distributions over two-dimensional plane with given mean values as convex combinations of distributions with supports containing not more than three points and with the same mean values.
Using the LePage representation, a strictly stable random element in a Banach space with $\alpha\in(0,2)$ can be represented as a sum of points of a Poisson process. This point process is union-stable, i.e. the union of its two independent…
The average density of zeros for monic generalized polynomials, $P_n(z)=\phi(z)+\sum_{k=1}^nc_kf_k(z)$, with real holomorphic $\phi ,f_k$ and real Gaussian coefficients is expressed in terms of correlation functions of the values of the…