Related papers: Characteristic polynomial of generalized Ewens ran…
Using the simple procedure, recently introduced, of dividing Gaussian matrices by a positive random variable, a family of random matrices is generated characterized by a behavior ruled by the generalized hyperbolic distribution. The…
Colored multiset Eulerian polynomials are a common generalization of MacMahon's multiset Eulerian polynomials and the colored Eulerian polynomials, both of which are known to satisfy well-studied distributional properties including…
We analyze a class of parametrized Random Matrix models, introduced by Rosenzweig and Porter, which is expected to describe the energy level statistics of quantum systems whose classical dynamics varies from regular to chaotic as a function…
Consider the ensemble of Real Symmetric Toeplitz Matrices, each entry iidrv from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. The limiting spectral measure (the density of normalized eigenvalues)…
We construct the general permutation invariant Gaussian 2-matrix model for matrices of arbitrary size $D$. The parameters of the model are given in terms of variables defined using the representation theory of the symmetric group $S_D$. A…
Non-Gaussian outcomes are often modeled using members of the so-called exponential family. Notorious members are the Bernoulli model for binary data, leading to logistic regression, and the Poisson model for count data, leading to Poisson…
The distribution of the characteristic polynomial $Z(U,\theta)$ of $N\times N$ matrices $U$ in the Circular Unitary Ensemble is studied by the method of second quantization for one-dimensional fermions. For infinite $N$ the Gaussian…
Applying E. Kowalski's recent generalization of the large sieve we prove that certain properties expected to be typical (irreducibility of the characteristic polynomial, absence of squares among the matrix coefficients...) are indeed…
We compute correlation functions of inverse powers and ratios of characteristic polynomials for random matrix models with complex eigenvalues. Compact expressions are given in terms of orthogonal polynomials in the complex plane as well as…
In this paper, we introduce a convergence notion for ordered selections. Our convergence notion is based on subpermutation densities and convergences of the marginal distributions. A particular case of this convergence is the well-known…
We investigate the eigenvalues statistics of ensembles of normal random matrices when their order N tends to infinite. In the model the eigenvalues have uniform density within a region determined by a simple analytic polynomial curve. We…
A family of consistent tests, derived from a characterization of the probability generating function, is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted…
We consider the asymptotics of the correlation functions of the characteristic polynomials of the hermitian Wigner matrices $H_n=n^{-1/2}W_n$. We show that for the correlation function of any even order the asymptotic coincides with this…
A single permutation, seen as union of disjoint cycles, represents a regular graph of degree two. Consider $d$ many independent random permutations and superimpose their graph structures. It is a common model of a random regular (multi-)…
We show that the linear statistics of eigenvalues of circulant matrix obey the Gaussian central limit theorem for a large class of input sequences.
The eigenvalues of quantum chaotic systems have been conjectured to follow, in the large energy limit, the statistical distribution of eigenvalues of random ensembles of matrices of size $N\rightarrow\infty$. Here we provide semiclassical…
We study the asymptotic behavior of short cycles of random permutations with cycle weights. More specifically, on a specially constructed metric space whose elements encode all possible cycles, we consider a point process containing all…
The singular values of products of standard complex Gaussian random matrices, or sub-blocks of Haar distributed unitary matrices, have the property that their probability distribution has an explicit, structured form referred to as a…
We consider the asymptotic local behavior of the second correlation functions of the characteristic polynomials of a certain class of Gaussian $N\times N$ non-Hermitian random band matrices with a bandwidth $W$. Given $W,N\to\infty$, we…
It has been shown recently [10] that Cauchy transforms of orthogonal polynomials appear naturally in general correlation functions containing ratios of characteristic polynomials of random NxN Hermitian matrices. Our main goal is to…