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Given a variety over $\mathbb{Q}$, we study the distribution of the number of primes dividing the coordinates as we vary an integral point. Under suitable assumptions, we show that this has a multivariate normal distribution. We generalise…
We study the singularity probability of n*n random matrices with i.i.d. entries from highly biased discrete distributions. We obtain sharp non-asymptotic bounds for this probability and derive estimates on the least singular values. Our…
We study the differential and metric structures of the set of real square roots of a non-singular real matrix, under the assumption that the matrix and its square roots are semi-simple, or symmetric, or orthogonal.
We study the scattering of waves in systems with losses or gains simulated by imaginary potentials. This is done for a complex delta potential that corresponds to a spatially localized absorption or amplification. In the Argand plane the…
We construct the multivariate probability distributions (P\'olya, inverse P\'olya, hypergeometric and negative hypergeometric) from the generalized quantum algebra. Moreover, we derive the bivariate probability distributions and determine…
In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also…
A new two-parameter discrete distribution, namely the PoiG distribution is derived by the convolution of a Poisson variate and an independently distributed geometric random variable. This distribution generalizes both the Poisson and…
Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics, etc., to name but a few) and the bivariate Poisson distribution which is a generalization of the Poisson distribution plays an…
In this paper we study the distribution of the scaled largest eigenvalue of complexWishart matrices, which has diverse applications both in statistics and wireless communications. Exact expressions, valid for any matrix dimensions, have…
We propose a multivariate probability distribution for categorical and ordinal random variables. To this end, we use the Grassmann distribution in conjunction with dummy encoding of categorical and ordinal variables. To realize the…
We consider the problem of estimating covariance and precision matrices, and their associated discriminant coefficients, from normal data when the rank of the covariance matrix is strictly smaller than its dimension and the available sample…
The aim of this paper is to study the mixture of the Riesz distribution on symmetric matrices with respect to the multivariate Poisson distribution. We show, in particular, that this distribution is related to the modified Bessel function…
We present a Gaussian ensemble of random cyclic matrices on the real field and study their spectral fluctuations. These cyclic matrices are shown to be pseudo-symmetric with respect to generalized parity. We calculate the joint probability…
A multifractal analysis is performed on the universality classes of random matrices and the transition ones.Our results indicate that the eigenvector probability distribution is a linear sum of two chi-squared distribution throughout the…
A three-parameter discrete distribution is developed to describe the multiplicity distributions observed in total- and limited phase space volumes in different collision processes. The probability law is obtained by the Poisson transform of…
We compute the joint distributions of arbitrary numbers of eigenvectors of real and complex symmetric random tensors by the quantum field theoretical methods which were previously used to compute the mean distributions. We obtain the random…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
We present a concentration inequality for linear functionals of noncommutative polynomials in random matrices. Our hypotheses cover most standard ensembles, including Gaussian matrices, matrices with independent uniformly bounded entries…
Classical random matrix ensembles with orthogonal symmetry have the property that the joint distribution of every second eigenvalue is equal to that of a classical random matrix ensemble with symplectic symmetry. These results are shown to…
The paper considers multivariate discrete random sums with equal number of summands. Such distributions describe the total claim amount received by a company in a fixed time point. In Queuing theory they characterize cumulative waiting…