Related papers: On Generalized Weighted Hilbert Matrices
In this work we show how to get advantage from the Riemann--Hilbert analysis in order to obtain first and second order differential equations for the orthogonal polynomials and associated functions with a weight on the unit circle. We…
In this article, we study properties of the exponential Hilbert series of a $G$-equivariant projective variety, where $G$ is a semisimple, simply-connected complex linear algebraic group. We prove a relationship between the exponential…
In these notes we review recent progress (and, in Section \ref{sec:ados}, we announce a new result) concerning the statistical properties of the spectrum of Wigner random matrices.
We investigate the properties of positive definite and positive semi-definite symmetric matrices within the framework of symmetrized tropical algebra, an extension of tropical algebra adapted to ordered valued fields. We focus on the…
For a large class of linear neutral type systems the problem of eigenvalues and eigenvectors assignment is investigated, i.e. finding the system which has the given spectrum and almost all, in some sense, eigenvectors.
In this survey paper we review classical results and recent progress about a certain topic in the spectral theory of two-dimensional canonical systems. Namely, we consider the questions whether the spectrum $\sigma$ is discrete, and if it…
In this study, we present a new generalization of circulant matrices for the generalized $k$-Horadam numbers, by considering the $g$-circulant matrix $C_{n,g}(H)=g -circ(H_{k,1},H_{k,2},\ldots ,H_{k,n})$. Also, we calculate the spectral…
In this paper, we explain the dependance of the fluctuations of the largest eigenvalues of a Deformed Wigner model with respect to the eigenvectors of the perturbation matrix. We exhibit quite general situations that will give rise to…
In the first part of these notes, we review some of the recent developments in the study of the spectral properties of Wigner matrices. In the second part, we present a new proof of a Wegner estimate for the eigenvalues of a large class of…
We consider a product of an arbitrary number of independent rectangular Gaussian random matrices. We derive the mean densities of its eigenvalues and singular values in the thermodynamic limit, eventually verified numerically. These…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
In this article we consider the spectrum of a Laplacian matrix, also known as the Markov matrix, under the independence assumption. We assume that the entries have a variance profile. Motivated by recent works on generalized Wigner matrices…
We study large deviation properties of random matricial spectral measures.
The complex Ginibre ensemble is an $N\times N$ non-Hermitian random matrix over $\mathbb{C}$ with i.i.d. complex Gaussian entries normalized to have mean zero and variance $1/N$. Unlike the Gaussian unitary ensemble, for which the…
Universality of eigenvalue spacings is one of the basic characteristics of random matrices. We give the precise meaning of universality and discuss the standard universality classes (sine, Airy, Bessel) and their appearance in unitary,…
We consider the single eigenvalue fluctuations of random matrices of general Wigner-type, under a one-cut assumption on the density of states. For eigenvalues in the bulk, we prove that the asymptotic fluctuations of a single eigenvalue…
In this paper, we introduce a particular class of matrices. We study the concept of a matrix to be \emph{balanced}. We study some properties of this concept in the context of matrix operations. We examine the behaviour of various matrix…
As is widely known, a non-Hermitian matrix exhibits distinct left and right eigenvectors, which form a bi-orthogonal system. Chalker and Mehling initiated the study of the joint statistics of the eigenvalues and the overlaps defined by the…
Spectral properties of Hermitian Toeplitz, Hankel, and Toeplitz-plus-Hankel random matrices with independent identically distributed entries are investigated. Combining numerical and analytic arguments it is demonstrated that spectral…
We prove a general local law for Wigner matrices which optimally handles observables of arbitrary rank and thus it unifies the well-known averaged and isotropic local laws. As an application, we prove that the quadratic forms of a general…