Related papers: Random Matrix Spectra as a Time Series
The eigenvalues of quantum chaotic systems have been conjectured to follow, in the large energy limit, the statistical distribution of eigenvalues of random ensembles of matrices of size $N\rightarrow\infty$. Here we provide semiclassical…
In this paper, High-dimensional data analysis methods are proposed to deal with random matrix which is composed by the real data from power network before and after the fault. The mean spectral radius (MSR) of non-Hermitian random matrices…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
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…
The paper studies processes defined on time domains structured as oriented spatial graphs (or metric graphs, or oriented branched 1-manifolds). This setting can be used, for example, for forecasting models involving branching scenarios. For…
Time series are collected and studied extensively for the knowledge about the data source characteristics such as the trend or the spectral landscape. Some peaks in the spectral landscape correspond to dominant frequencies. The approach…
We observe returns of a simple random walk on a finite graph to a fixed node, and would like to infer properties of the graph, in particular properties of the spectrum of the transition matrix. This is not possible in general, but at least…
The classical Fourier analysis of a time signal, in the discrete sense, provides the frequency content of signal under the assumption of periodicity. Although the original signal can be exactly recovered using an inverse transform, the time…
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…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
Many time series in smart energy systems exhibit two different timescales. On the one hand there are patterns linked to daily human activities. On the other hand, there are relatively slow trends linked to seasonal variations. In this paper…
Many complex systems can be reduced to their key components through spectrally decomposing matrices that capture their dynamics. These matrices can in turn be constructed from data, often by least-squares fitting: examples of algorithms to…
We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…
Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact…
We study spectral densities for systems on lattices, which, at a phase transition display, power-law spatial correlations. Constructing the spatial correlation matrix we prove that its eigenvalue density shows a power law that can be…
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 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…
Analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle are developed. Vandermonde Matrices play an important role in signal processing and wireless applications such as direction of arrival…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
We obtain sequences of inclusion sets for the spectrum, essential spectrum, and pseudospectrum of banded, in general non-normal, matrices of finite or infinite size. Each inclusion set is the union of the pseudospectra of certain…