Related papers: Spectral Density Scaling of Fluctuating Interfaces
We compute spectra of sample auto-covariance matrices of second order stationary stochastic processes. We look at a limit in which both the matrix dimension $N$ and the sample size $M$ used to define empirical averages diverge, with their…
Applying the replica method of statistical mechanics, we evaluate the eigenvalue density of the large random matrix (sample covariance matrix) of the form $J = A^{\rm T} A$, where $A$ is an $M \times N$ real sparse random matrix. The…
We study the spectra and eigenvectors of the adjacency matrices of scale-free networks when bi-directional interaction is allowed, so that the adjacency matrix is real and symmetric. The spectral density shows an exponential decay around…
We present an exact solution for the distribution P(h_m,L) of the maximal height h_m (measured with respect to the average spatial height) in the steady state of a fluctuating Edwards-Wilkinson interface in a one dimensional system of size…
The eigenvalues and eigenvectors of the connectivity matrix of complex networks contain information about its topology and its collective behavior. In particular, the spectral density $\rho(\lambda)$ of this matrix reveals important network…
The asymptotic behaviour of Linear Spectral Statistics (LSS) of the smoothed periodogram estimator of the spectral coherency matrix of a complex Gaussian high-dimensional time series $(\y_n)_{n \in \mathbb{Z}}$ with independent components…
The salient properties of large empirical covariance and correlation matrices are studied for three datasets of size 54, 55 and 330. The covariance is defined as a simple cross product of the returns, with weights that decay logarithmically…
The spectral density of various ensembles of sparse symmetric random matrices is analyzed using the cavity method. We consider two cases: matrices whose associated graphs are locally tree-like, and sparse covariance matrices. We derive a…
We apply random matrix theory to derive spectral density of large sample covariance matrices generated by multivariate VMA(q), VAR(q) and VARMA(q1,q2) processes. In particular, we consider a limit where the number of random variables N and…
In this paper, we study the convergence rates of empirical spectral distribution of large dimensional quaternion sample covariance matrix. Assume that the entries of $\mathbf X_n$ ($p\times n$) are independent quaternion random variables…
Consider the random matrix $\Sigma = D^{1/2} X \widetilde D^{1/2}$ where $D$ and $\widetilde D$ are deterministic Hermitian nonnegative matrices with respective dimensions $N \times N$ and $n \times n$, and where $X$ is a random matrix with…
In this paper the question about statistical properties of block--hierarchical random matrices is raised for the first time in connection with structural characteristics of random hierarchical networks obtained by mipmapping procedure. In…
We demonstrate that the normalised localization length $\beta$ of the eigenfunctions of diluted (sparse) banded random matrices follows the scaling law $\beta=x^*/(1+x^*)$. The scaling parameter of the model is defined as…
A method for measuring the spectrum of a density field by a discrete wavelet space-scale decomposition (SSD) has been studied. We show how the power spectrum can effectively be described by the father function coefficients (FFC) of the…
The asymptotic behaviour of Linear Spectral Statistics (LSS) of the smoothed periodogram estimator of the spectral coherency matrix of a complex Gaussian high-dimensional time series $(\y_n)_{n \in \mathbb{Z}}$ with independent components…
We present a detailed study of squared local roughness (SLRDs) and local extremal height distributions (LEHDs), calculated in windows of lateral size $l$, for interfaces in several universality classes, in substrate dimensions $d_s = 1$ and…
A recently proposed linear-scaling scheme for density-functional pseudopotential calculations is described in detail. The method is based on a formulation of density functional theory in which the ground state energy is determined by…
We investigate joint spectral characteristics of a family of matrices $\mathcal F $, associated with products in the semigroup generated by $\mathcal F$. In the literature, extremal measures such as the well-known joint spectral radius and…
We consider the eigenvalues of sample covariance matrices of the form $\mathcal{Q}=(\Sigma^{1/2}X)(\Sigma^{1/2}X)^*$. The sample $X$ is an $M\times N$ rectangular random matrix with real independent entries and the population covariance…
In this paper, we study the fluctuation of linear eigenvalue statistics of Random Band Matrices defined by $M_{n}=\frac{1}{\sqrt{b_{n}}}W_{n}$, where $W_{n}$ is a $n\times n$ band Hermitian random matrix of bandwidth $b_{n}$, i.e., the…