Related papers: Eigenvalues of random matrices with generalised co…
We consider the correlation functions of eigenvalues of a unidimensional chain of large random hermitian matrices. An asymptotic expression of the orthogonal polynomials allows to find new results for the correlations of eigenvalues of…
The eigenvalue spectrum of the transition matrix of a network encodes important information about its structural and dynamical properties. We study the transition matrix of a family of fractal scale-free networks and analytically determine…
We consider random non-normal matrices constructed by removing one row and column from samples from Dyson's circular ensembles or samples from the classical compact groups. We develop sparse matrix models whose spectral measures match these…
A method of resummation of infinite series of perturbation theory diagrams is applied for studying the properties of random band matrices. The topological classification of Feynman diagrams, which was actively used in last years for matrix…
A large variety of dynamical processes that take place on networks can be expressed in terms of the spectral properties of some linear operator which reflects how the dynamical rules depend on the network topology. Often such spectral…
Eigenvalue correlations of random matrix ensembles as a function of an external perturbation are investigated vis the Dyson Brownian Motion Model in the situation where the level density has a hard edge singularity. By solving a linearized…
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…
The article attempts to find an algebraic formula describing the correlation coefficients between random variables and the principal components representing them. As a result of the analysis, starting from selected statistics relating to…
Estimating the eigenvalues of a population covariance matrix from a sample covariance matrix is a problem of fundamental importance in multivariate statistics; the eigenvalues of covariance matrices play a key role in many widely…
We analyze complex networks under random matrix theory framework. Particularly, we show that $\Delta_3$ statistic, which gives information about the long range correlations among eigenvalues, provides a qualitative measure of randomness in…
This review article provides an overview of random matrix theory (RMT) with a focus on its growing impact on the formulation and inference of statistical models and methodologies. Emphasizing applications within high-dimensional statistics,…
We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such…
We derive the distribution of eigenvalues of the reduced density matrix of a block of length l in a one-dimensional system in the scaling regime. The resulting "entanglement spectrum" is described by a universal scaling function depending…
In general or normal random matrix ensembles, the support of eigenvalues of large size matrices is a planar domain (or several domains) with a sharp boundary. This domain evolves under a change of parameters of the potential and of the size…
A feature of certain ensembles of random matrices is that the corresponding measure is invariant under conjugation by unitary matrices. Study of such ensembles realised by matrices with Gaussian entries leads to statistical quantities…
The eigenvalue spectrum of the sum of large random matrices that are mutually "free", i.e., randomly rotated, can be obtained using the formalism of R-transforms, with many applications in different fields. We provide a direct…
We propose a theoretical framework to study the eigenvalue spectra of the controllability Gramian of systems with random state matrices, such as networked systems with a random graph structure. Using random matrix theory, we provide…
We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson…
We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of our work will appear soon in separate publications.) Following an introduction of…
We consider the eigenvalues and eigenvectors of finite, low rank perturbations of random matrices. Specifically, we prove almost sure convergence of the extreme eigenvalues and appropriate projections of the corresponding eigenvectors of…