Related papers: Generic Features in the Spectral Decomposition of …
We consider low--dimensional dynamical systems with a mixed phase space and discuss the typical appearance of slow, polynomial decay of correlations: in particular we emphasize how this mixing rate is related to large deviations properties.
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…
Non-Hermitian random matrices with statistical spectral characteristics beyond the standard Ginibre ensembles have recently emerged in the description of dissipative quantum many-body systems as well as in non-ergodic wave transport in…
In this paper, we show that the diagonal of a high-dimensional sample covariance matrix stemming from $n$ independent observations of a $p$-dimensional time series with finite fourth moments can be approximated in spectral norm by the…
In an attempt to characterize the structure of eigenvectors of random regular graphs, we investigate the correlations between the components of the eigenvectors associated to different vertices. In addition, we provide numerical…
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…
We study some properties of eigenvalue spectra of financial correlation matrices. In particular, we investigate the nature of the large eigenvalue bulks which are observed empirically, and which have often been regarded as a consequence of…
We develop a supersymmetric field theoretical description of the Gaussian ensemble of the almost diagonal Hermitian Random Matrices. The matrices have independent random entries H_{ij} with parametrically small off-diagonal elements…
In this paper, we study the empirical spectral distribution of Spearman's rank correlation matrices, under the assumption that the observations are independent and identically distributed random vectors and the features are correlated. We…
In this paper, we consider the empirical spectral distribution of the sample correlation matrix and investigate its asymptotic behavior under mild assumptions on the data's distribution, when dimension and sample size increase at the same…
We investigate almost-degenerate perturbation theory of eigenvalue problems, using spectral projectors, also named density matrices. When several eigenvalues are close to each other, the coefficients of the perturbative series become…
A basic fact in spectral graph theory is that the number of connected components in an undirected graph is equal to the multiplicity of the eigenvalue zero in the Laplacian matrix of the graph. In particular, the graph is disconnected if…
We define a graph to be $S$-regular if it contains an equitable partition given by a matrix $S$. These graphs are generalizations of both regular and bipartite, biregular graphs. An $S$-regular matrix is defined then as a matrix on an…
We prove delocalization of eigenvectors of vertex-transitive graphs via elementary estimates of the spectral projector. We recover in this way known results which were formerly proved using representation theory. Similar techniques show…
A generalized Wigner matrix perturbed by a finite-rank deterministic matrix is considered. The fluctuations of the largest eigenvalues, which emerge outside the bulk of the spectrum, and the corresponding eigenvectors, are studied. Under…
Here, the structural symmetries of a hypergraph are represented through equivalence relations on the vertex set of the hypergraph. A matrix associated with the hypergraph may not reflect a specific structural symmetry. In the context of a…
The paper presents a general theory of coupling of eigenvalues of complex matrices of arbitrary dimension depending on real parameters. The cases of weak and strong coupling are distinguished and their geometric interpretation in two and…
For a large class of quantum systems the statistical properties of their spectrum show remarkable agreement with random matrix predictions. Recent advances show that the scope of random matrix theory is much wider. In this work, we show…
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
In this article, we establish a limiting distribution for eigenvalues of a class of auto-covariance matrices. The same distribution has been found in the literature for a regularized version of these auto-covariance matrices. The original…