Related papers: Surmise for random matrices' level spacing distrib…
We study the distribution of non-overlapping spacing ratios of higher-orders for complex interacting many-body quantum systems, with and without spin degree of freedom (in addition to the particle number). The Hamiltonian of such systems is…
We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest- and…
We investigate the level spacing distribution for three ensembles of real symmetric matrices having additional structural constraint to reduce the number of independent entries to only $ (n+1)/2 $ in contrast to the $ n(n+1)/2 $ for a real…
The Wigner spacing distribution has a long and illustrious history in nuclear physics and in the quantum mechanics of classically chaotic systems. In this paper, a novel connection between the Wigner distribution and 2D classical mechanics…
The nearest-neighbor mass-spacing distribution of the meson and baryon spectrum (up to 2.5 GeV) is described by the Wigner surmise corresponding to the statistics of the Gaussian orthogonal ensemble of random matrix theory. This can be…
The discrete distribution of the length of longest increasing subsequences in random permutations of $n$ integers is deeply related to random matrix theory. In a seminal work, Baik, Deift and Johansson provided an asymptotics in terms of…
Finding an approximation of the inverse of the covariance matrix, also known as precision matrix, of a random vector with empirical data is widely discussed in finance and engineering. In data-driven problems, empirical data may be…
Level statistics is discussed for XXZ spin chains with discrete symmetries for some values of the next-nearest-neighbor (NNN) coupling parameter. We show how the level statistics of the finite-size systems depends on the NNN coupling and…
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…
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…
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…
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 statistics of gap ratios between consecutive energy levels is a widely used tool, in particular in the context of many-body physics, to distinguish between chaotic and integrable systems, described respectively by Gaussian ensembles of…
The simple one-parameter nearest neighbor-spacing distribution (NNSD) is suggested for statistical analysis of nuclear spectra. This distribution is derived within the Wigner-Dyson approach in the linear approximation for the level…
This paper addresses the problem of quickest detection of a change in the maximal coherence between columns of a $n\times p$ random matrix based on a sequence of matrix observations having a single unknown change point. The random matrix is…
The ratio of two consecutive level spacings has emerged as a very useful metric in investigating universal features exhibited by complex spectra. It does not require the knowledge of density of states and is therefore quite convenient to…
The distribution of the consecutive level-spacing ratio is now widely used as a tool to distinguish integrable from chaotic quantum spectra, mostly due to its avoiding of the numerical spectral unfolding. Similar to the use of the…
The level-spacing distributions of XXZ spin chains with next-nearest-neighbor couplings are studied under periodic boundary conditions. We confirm that integrable XXZ spin chains mostly have the Poisson distribution as expected. On the…
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…
We study a class of Hermitian random matrices which includes and generalizes Wigner matrices, heavy-tailed random matrices, and sparse random matrices such as the adjacency matrices of Erdos-Renyi random graphs with p ~ 1/N. Our NxN random…