相关论文: Statistical properties of random density matrices

We study the probability measure on the space of density matrices induced by the metric defined by using superfidelity. We give the formula for the probability density of eigenvalues. We also study some statistical properties of the set of…

The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/Sqrt(2N), where N is the size of the matrix, in the large…

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,…

For a broad class of unitary ensembles of random matrices we demonstrate the universal nature of the Janossy densities of eigenvalues near the spectral edge, providing a different formulation of the probability distributions of the limiting…

We compute the distribution of the number of negative eigenvalues (the index) for an ensemble of Gaussian random matrices, by means of the replica method. This calculation has important applications in the context of statistical mechanics…

We describe Generalized Hermitian matrices ensemble sometimes called Chiral ensemble. We give global asymptotic of the density of eigenvalues or the statistical density. We will calculate a Laplace transform of such a density for finite…

We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit…

We consider large non-Hermitian real or complex random matrices $X$ with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of…

The joint eigenvalue distributions of random-matrix ensembles are derived by applying the principle maximum entropy to the Renyi, Abe and Kaniadakis entropies. While the Renyi entropy produces essentially the same matrix-element…

We investigate the eigenvalue statistics of random Bernoulli matrices, where the matrix elements are chosen independently from a binary set with equal probability. This is achieved by initiating a discrete random walk process over the space…

We revisit the derivation of the density of states of sparse random matrices. We derive a recursion relation that allows one to compute the spectrum of the matrix of incidence for finite trees that determines completely the low…

We equip the polytope of $n\times n$ Markov matrices with the normalized trace of the Lebesgue measure of $\mathbb{R}^{n^2}$. This probability space provides random Markov matrices, with i.i.d. rows following the Dirichlet distribution of…

Statistical ensembles of reduced density matrices of bipartite quantum systems play a central role in entanglement estimation, but do not capture the non-stationary nature of entanglement relevant to realistic quantum information…

Spectral and numerical properties of classes of random orthogonal butterfly matrices, as introduced by Parker (1995), are discussed, including the uniformity of eigenvalue distributions. These matrices are important because the…

We discuss an application of the random matrix theory in the context of estimating the bipartite entanglement of a quantum system. We discuss how the Wishart ensemble (the earliest studied random matrix ensemble) appears in this quantum…

In this article, we study microscopic properties of a two-dimensional eigenvalue ensemble near a conical singularity arising from insertion of a point charge in the bulk of the support of eigenvalues. In particular, we characterize all…

Composed ensembles of random unitary matrices are defined via products of matrices, each pertaining to a given canonical circular ensemble of Dyson. We investigate statistical properties of spectra of some composed ensembles and demonstrate…

We compute analytically the joint probability density of eigenvalues and the level spacing statistics for an ensemble of random matrices with interesting features. It is invariant under the standard symmetry groups (orthogonal and unitary)…

A quantum statistical system with energy dissipation is studied. Its statisitics is governed by random complex-valued non-Hermitean Hamiltonians belonging to complex Ginibre ensemble. The eigenenergies are shown to form stable structure in…

The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…