Related papers: Statistics of Atmospheric Correlations
The formation of aerosol particles in the atmosphere impacts air quality and climate change, but many of the organic molecules involved remain unknown. Machine learning could aid in identifying these compounds through accelerated analysis…
Exploring exoplanets has transformed our understanding of the universe by revealing many planetary systems that defy our current understanding. To study their atmospheres, spectroscopic observations are used to infer essential atmospheric…
The entanglement spectrum, i.e., the full distribution of Schmidt eigenvalues of the reduced density matrix, contains more information than the conventional entanglement entropy and has been studied recently in several many-particle…
Spectra of ordered eigenvalues of finite Random Matrices are interpreted as a time series. Dataadaptive techniques from signal analysis are applied to decompose the spectrum in clearly differentiated trend and fluctuation modes, avoiding…
Multivariate spatial phenomena are ubiquitous, spanning domains such as climate, pandemics, air quality, and social economy. Cross-correlation between different quantities of interest at different locations is asymmetric in general. This…
The apparent randomness of chaotic eigenstates in interacting quantum systems hides subtle correlations dynamically imposed by their finite energy per particle. These correlations are revealed when Berrys approach for chaotic eigenfunctions…
In this paper, we show that the diagonal of a high-dimensional sample covariance matrix stemming from $n$ independent observations of a $p$-dimensional time series with finite fourth moments can be approximated in spectral norm by the…
The operating status of power systems is influenced by growing varieties of factors, resulting from the developing sizes and complexity of power systems; in this situation, the modelbased methods need be revisited. A data-driven method, as…
Contact has been well established as an important quantity to govern dilute quantum systems, in which the pairwise correlation at short distance traces a broad range of thermodynamic properties. So far, studies have been focusing on contact…
It is known that hermitean random matrix ensembles can be identified with symmetric coset spaces of Lie groups, or else with tangent spaces of the same. This results in a classification of random matrix ensembles as well as applications in…
An empirical model is a generalization of a probability space. It consists of a simplicial complex of subsets of a class X of random variables such that each simplex has an associated probability distribution. The ensuing marginalizations…
In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…
The topic of this paper is the typical behavior of the spectral measures of large random matrices drawn from several ensembles of interest, including in particular matrices drawn from Haar measure on the classical Lie groups, random…
Random matrix theory is finding an increasing number of applications in the context of information theory and communication systems, especially in studying the properties of complex networks. Such properties include short-term and long-term…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
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…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
The application of random matrix theory to scattering requires introduction of system-specific information. This paper shows that the average impedance matrix, which characterizes such system-specific properties, can be semiclassically…
We compare the statistical fluctuation properties of the baryon and meson experimental mass spectra with those obtained from theoretical models (quark models and lattice QCD). We find that for the experimental spectra the statistical…
We discuss a practical method to determine the eigenvalue spectrum of the empirical correlation matrix. The method is based on the analysis of the behavior of a conformal map at a critical horizon which is defined as a border line of the…