Related papers: Scaling in the eigenvalue fluctuations of the empi…
The distribution of the ratios of nearest neighbor level spacings has become a popular indicator of spectral fluctuations in complex quantum systems like interacting many-body localized and thermalization phases, quantum chaotic systems,…
The connection between random matrices and the spectral fluctuations of complex quantum systems in a suitable limit can be explained by using the setup of random matrix theory. Higher-order spacing statistics in the $m$ superposed spectra…
The statistical properties of spectra of quantum systems within the framework of random matrix theory is widely used in many areas of physics. These properties are affected, if two or more sets of spectra are superposed, resulting from the…
Wishart random matrix theory is of major importance for the analysis of correlated time series. The distribution of the smallest eigenvalue for Wishart correlation matrices is particularly interesting in many applications. In the complex…
Recent advances in random matrix theory have spurred the adoption of eigenvalue-based detection techniques for cooperative spectrum sensing in cognitive radio. Most of such techniques use the ratio between the largest and the smallest…
A Wishart matrix is said to be spiked when the underlying covariance matrix has a single eigenvalue $b$ different from unity. As $b$ increases through $b=2$, a gap forms from the largest eigenvalue to the rest of the spectrum, and with…
The correlated Wishart model provides a standard tool for the analysis of correlations in a rich variety of systems. Although much is known for complex correlation matrices, the empirically much more important real case still poses…
We study random points on the real line generated by the eigenvalues in unitary invariant random matrix ensembles or by more general repulsive particle systems. As the number of points tends to infinity, we prove convergence of the…
Efficient schemes for sampling from the eigenvalues of the Wishart distribution have recently been described for both the uncorrelated central case (where the covariance matrix is $\mathbf{I}$) and the spiked Wishart with a single spike…
In this paper, we consider the problem of deriving new eigenvalue distributions of real-valued Wishart matrices that arises in many scientific and engineering applications. The distributions are derived using the tools from the theory of…
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 reduced energy spectrum $\{E_{i}^{(n)}\}$, which is constructed by picking one level from every $n$ levels of the original spectrum $\{E_{i}\}$, in a Gaussian ensemble of random matrix with Dyson index $\beta\in \left( 0,\infty…
Vinberg cones and the ambient vector spaces are important in modern statistics of sparse models and of graphical models. The aim of this paper is to study eigenvalue distributions of Gaussian, Wigner and covariance matrices related to…
The distribution of higher order level spacings, i.e. the distribution of $\{s_{i}^{(n)}=E_{i+n}-E_{i}\}$ with $n\geq 1$ is derived analytically using a Wigner-like surmise for Gaussian ensembles of random matrix as well as Poisson…
The distribution of the ratios of consecutive eigenvalue spacings of random matrices has emerged as an important tool to study spectral properties of many-body systems. This article numerically investigates the eigenvalue ratios…
Previous literature on random matrix and network science has traditionally employed measures derived from nearest-neighbor level spacing distributions to characterize the eigenvalue statistics of random matrices. This approach, however,…
The sum of independent Wishart matrices, taken from distributions with unequal covariance matrices, plays a crucial role in multivariate statistics, and has applications in the fields of quantitative finance and telecommunication. However,…
In this lecture we argue that the fluctuations of Dirac eigenvalues on the finest scale, i.e. on the scale of the average level spacing do not depend on the underlying dynamics and can be obtained from a chiral random matrix theory with the…
The correlated Wishart model provides the standard benchmark when analyzing time series of any kind. Unfortunately, the real case, which is the most relevant one in applications, poses serious challenges for analytical calculations. Often…
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…