Related papers: Level-spacing distribution of a fractal matrix
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
It is believed that the semi-Poisson function $P(S)=4S\exp(-2S)$ describes the normalized distribution of the nearest level-spacings $S$ for critical energy levels at the Anderson metal-insulator transition from quantum chaos to…
We study spectral behavior of sparsely connected random networks under the random matrix framework. Sub-networks without any connection among them form a network having perfect community structure. As connections among the sub-networks are…
Typical eigenstates of quantum systems, whose classical limit is chaotic, are well approximated as random states. Corresponding eigenvalue spectra is modeled through appropriate ensemble of random matrix theory. However, a small subset of…
We investigate the spread complexity of a generic two-level subsystem of a larger system to analyze the influence of energy level statistics, comparing chaotic and integrable systems. Initially focusing on the nearest-neighbor level…
Entanglement spectrum of finite-size correlated electron systems are investigated using the Gutzwiller projection technique. The product of largest eigenvalue and rank of the block reduced density matrix, which is a measure of distance of…
We analyse the eigenvectors of the adjacency matrix of a random inhomogeneous graph constructed from a specified degree sequence. We assume that the empirical degree sequence has bounded mean and variance. We show that near the edges of the…
We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is…
The nearest-neighbor level spacing distribution is numerically investigated by directly diagonalizing disordered Anderson Hamiltonians for systems of sizes up to 100 x 100 x 100 lattice sites. The scaling behavior of the level statistics is…
The level spacing distributions which arise when one rescales the Laguerre or Jacobi ensembles of hermitian matrices is studied. These distributions are expressible in terms of a Fredholm determinant of an integral operator whose kernel is…
In this paper, we characterize the convergence of the (rescaled logarithmic) empirical spectral distribution of wavelet random matrices. We assume a moderately high-dimensional framework where the sample size $n$, the dimension $p(n)$ and,…
We study random normal matrix models whose eigenvalues tend to be distributed within a narrow "band" around the unit circle of width proportional to $\frac1n$, where $n$ is the size of matrices. For general radially symmetric potentials…
The Nearest Neighbour Spacing (NNS) distribution can be computed for generalized symmetric 2x2 matrices having different variances in the diagonal and in the off-diagonal elements. Tuning the relative value of the variances we show that the…
We consider $N\times N$ Hermitian random matrices with i.i.d. entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order $1/N$. We study the connection between eigenvalue statistics on…
We study the statistics of level spacing of geometric resonances in the disordered binary networks. For a definite concentration $p$ within the interval $[0.2,0.7]$, numerical calculations indicate that the unfolded level spacing…
We study the probability distribution of the ratio of consecutive level spacings for embedded one plus two-body random matrix ensembles with and without spin degree of freedom and for both fermion and boson systems. The agreement between…
We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…
We study spectra and localization properties of Euclidean random matrices. The problem is approximately mapped onto that of a matrix defined on a random graph. We introduce a powerful method to find the density of states and the…
The intensity distribution of electromagnetic polar waves in a chain of near-resonant weakly-coupled scatterers is investigated theoretically and supported by a numerical analysis. Critical scaling behavior is discovered for part of the…
This paper presents a diffusion based probabilistic interpretation of spectral clustering and dimensionality reduction algorithms that use the eigenvectors of the normalized graph Laplacian. Given the pairwise adjacency matrix of all…