Related papers: Surmise for random matrices' level spacing distrib…
We present new analytical results concerning the spectral distributions for 2x2 random real symmetric matrices which generalise the Wigner surmise.
We study the problem of distributional matrix completion: Given a sparsely observed matrix of empirical distributions, we seek to impute the true distributions associated with both observed and unobserved matrix entries. This is a…
We consider a possible generalization of the random matrix theory, which involves the maximization of Tsallis' $q$-parametrized entropy. We discuss the dependence of the spacing distribution on $q$ using a non-extensive generalization of…
We derive an expression for the nearest-neighbor spacing distribution $P(s)$ of the energy levels of quantum systems with intermediate dynamics between regularity and chaos and missing levels due to random experimental errors. The…
Statistical analysis of distributions of the collective states in the actinide and rare-earth nuclei is performed in terms of the nearest neighbor spacing distribution (NNSD). Several approximations, such as the linear approach to the level…
We present a new approach, based on graphon theory, to finding the limiting spectral distributions of general Wigner-type matrices. This approach determines the moments of the limiting measures and the equations of their Stieltjes…
We consider nearest neighbor spacing distributions of composite ensembles of levels. These are obtained by combining independently unfolded sequences of levels containing only few levels each. Two problems arise in the spectral analysis of…
In this paper, we derive nearly tight probabilistic norm bounds for a class of random matrices we call graph matrices. While the classical case of symmetric matrices with independent random entries (Wigner's matrices) is a special case, in…
We study the nearest-neighbor distributions of the $k$-body embedded ensembles of random matrices for $n$ bosons distributed over two-degenerate single-particle states. This ensemble, as a function of $k$, displays a transition from…
We address overcrowding estimates for the singular values of random iid matrices, as well as for the eigenvalues of random Wigner matrices. We show evidence of long range separation under arbitrary perturbation even in matrices of discrete…
The problem of quickest detection of a change in the distribution of a $n\times p$ random matrix based on a sequence of observations having a single unknown change point is considered. The forms of the pre- and post-change distributions of…
Higher-order spacing ratios are investigated analytically using a Wigner-like surmise for Gaussian ensembles of random matrices. For $k$-th order spacing ratio $(r^{(k)}$, $k>1)$ the matrix of dimension $2k+1$ is considered. A universal…
We consider $N\times N$ Hermitian random matrices with independent identically distributed entries (Wigner matrices). The matrices are normalized so that the average spacing between consecutive eigenvalues is of order $1/N$. Under suitable…
We consider random Hermitian matrices with independent upper triangular entries. Wigner's semicircle law says that under certain additional assumptions, the empirical spectral distribution converges to the semicircle distribution. We…
The spectra of empirical correlation matrices, constructed from multivariate data, are widely used in many areas of sciences, engineering and social sciences as a tool to understand the information contained in typically large datasets. In…
We analyse the structure of the distribution of eigenvalues of the stock market correlation matrix with increasing length of the time series representing the price changes. We use 100 highly-capitalized stocks from the American market and…
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…
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…
The distribution of nuclear ground-state spin in the two-body random ensemble (TBRE) is studied by using a general classification neural network (NN) model with the two-body interaction matrix elements as input features and corresponding…
Quantum many-body systems are commonly considered as quantum chaotic if their spectral statistics, such as the level spacing distribution, agree with those of random matrix theory. Using the example of the kicked Ising chain we demonstrate…