Related papers: Doubly noncentral singular matrix variate beta dis…
Using operator methods, we generally present the level densities for kinds of random matrix unitary ensembles in weak sense. As a corollary, the limit spectral distributions of random matrices from Gaussian, Laguerre and Jacobi unitary…
We exhibit an explicit formula for the spectral density of a (large) random matrix which is a diagonal matrix whose spectral density converges, perturbated by the addition of a symmetric matrix with Gaussian entries and a given (small)…
This note provides some new inequalities and approximations for beta distributions, including tail inequalities, exponential inequalities of Hoeffding and Bernstein type, Gaussian inequalities and approximations.
The article is devoted to Beta and Gamma functions of Cayley-Dickson numbers. It is shown that there are specific features in comparison with the complex case. These functions serve as examples of meromorphic functions of Cayley-Dickson…
The polygonal distributions are a class of distributions that can be defined via the mixture of triangular distributions over the unit interval. The class includes the uniform and trapezoidal distributions, and is an alternative to the beta…
A fairly general procedure is studied to perturbate a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities. The approach is general enough to encompass a number of…
The probability distribution function (PDF) of the mass surface density of molecular clouds provides essential information about the structure of molecular cloud gas and condensed structures out of which stars may form. In general, the PDF…
This paper introduces a probability density estimator based on Green's function identities. A density model is constructed under the sole assumption that the probability density is differentiable. The method is implemented as a binary…
We consider a planar dynamical system generated by two stable linear vector fields with distinct fixed points and random switching between them. We characterize singularities of the invariant density in terms of the switching rates and…
We revisit scalar emissions in double beta decays of nuclei, often discussed in the context of Majoron models, in light of the latest developments on the study of neutrinoless double beta decay amplitudes from an effective field theory…
We consider the possibility that neutrinoless double beta decay may occur in models with unbroken lepton number via the emission of a massive gauge boson with electron lepton number $-2$. We determine the shape of the $\beta\,\beta$ sum…
For each $n$, let $A_n=(\sigma_{ij})$ be an $n\times n$ deterministic matrix and let $X_n=(X_{ij})$ be an $n\times n$ random matrix with i.i.d. centered entries of unit variance. In the companion article Cook et al., we considered the…
We analyze statistical properties of complex eigenvalues of random matrices $\hat{A}$ close to unitary. Such matrices appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with…
We extend the method of rescaled Ward identities of Ameur-Kang-Makarov to study the distribution of eigenvalues close to a bulk singularity, i.e. a point in the interior of the droplet where the density of the classical equilibrium measure…
In this paper we construct the new coefficient which allows to measure quantitatively the independence of the two discrete random variables. The new inequalities for the matrices with non-negative elements are found
Some properties of $m$-density points and density-degree functions are studied. Moreover the following main results are provided: \vskip2mm \begin{itemize} \item {\it Let $\lambda$ be a continuous differential form of degree $h$ in…
The eigenvalue densities of two random matrix ensembles, the Wigner Gaussian matrices and the Wishart covariant matrices, are decomposed in the contributions of each individual eigenvalue distribution. It is shown that the fluctuations of…
We compute the exact and limiting smallest eigenvalue distributions for two classes of $\beta$-Jacobi ensembles not covered by previous studies. In the general $\beta$ case, these distributions are given by multivariate hypergeometric…
The distribution functions of the matricvariate beta type I and II distributions are studied under real normed division algebras. The unified approach for real, complex, quaternions and octonions, also considers general properties and…
In this paper, the linear differential expression of order $n \ge 2$ with distribution coefficients of various singularity orders is considered. We obtain the associated matrix for the regularization of this expression. Furthermore, we…