相关论文: Universal and nonuniversal distant regional correl…
Electronic transport through chaotic quantum dots exhibits universal, system independent, properties, consistent with random matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over the…
We apply Tsallis's q-indexed nonextensive entropy to formulate a random matrix theory (RMT), which may be suitable for systems with mixed regular-chaotic dynamics. We consider the super-extensive regime of q < 1. We obtain analytical…
The cross-correlation matrix of daily returns of stock market indices in a diverse set of 37 countries worldwide was analyzed. Comparison of the spectrum of this matrix with predictions of random matrix theory provides an empirical evidence…
We present a new technique in order to quantify the dynamics of spatially extended systems. Using a test on the existence of unstable periodic orbits, we identify intermediate spatial scales, wherein the dynamics is characterized by maximum…
Every sufficiently big matrix with small spectral norm has a nearby low-rank matrix if the distance is measured in the maximum norm (Udell & Townsend, SIAM J Math Data Sci, 2019). We use the Hanson--Wright inequality to improve the estimate…
The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…
The concept of universality proposes that dynamical systems with the same power law behaviors are equivalent at large scales. We test this hypothesis on the Earth's crust and the epileptic brain, and discover that power laws also govern the…
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…
A paradigmatic framework to study the phenomenon of spontaneous collective synchronization is provided by the Kuramoto model comprising a large collection of limit-cycle oscillators of distributed frequencies that are globally coupled…
It is now a well-known fact that the correlations arising from local dichotomic measurements on an entangled quantum state may exhibit intrinsically non-classical features. In this paper we delve into a comprehensive study of random…
A novel non-parametric estimator of the correlation between grouped measurements of a quantity is proposed in the presence of noise. This work is primarily motivated by functional brain network construction from fMRI data, where brain…
This review article provides an overview of random matrix theory (RMT) with a focus on its growing impact on the formulation and inference of statistical models and methodologies. Emphasizing applications within high-dimensional statistics,…
In this article, a model of random hermitian matrices is considered, in which the measure $\exp(-S)$ contains a general U(N)-invariant potential and an external source term: $S=N\tr(V(M)+MA)$. The generalization of known determinant…
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…
The noncentral Wishart distribution has become more mainstream in statistics as the prevalence of applications involving sample covariances with underlying multivariate Gaussian populations as dramatically increased since the advent of…
In this paper we study a random matrix model with the chiral and flavor structure of the QCD Dirac operator and a temperature dependence given by the lowest Matsubara frequency. Using the supersymmetric method for random matrix theory, we…
We revisit the probabilistic construction of sparse random matrices where each column has a fixed number of nonzeros whose row indices are drawn uniformly at random with replacement. These matrices have a one-to-one correspondence with the…
This paper considers several aspects of random matrix universality in deep neural networks. Motivated by recent experimental work, we use universal properties of random matrices related to local statistics to derive practical implications…
In this work we investigate the phenomena associated with the new thresholds in the spectrum of excitations arising when different one-dimensional strongly interacting systems are voltage biased and weakly coupled by tunneling. We develop…
We address the quantum-classical correspondence for chaotic systems with a crossover between symmetry classes. We consider the energy level statistics of a classically chaotic system in a weak magnetic field. The generating function of…