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Random matrices whose entries come from a stationary Gaussian process are studied. The limiting behavior of the eigenvalues as the size of the matrix goes to infinity is the main subject of interest in this work. It is shown that the…
We describe a previously unexplored effect of the continuous spontaneous localization model whereby a correlation develops in the distributions of two nearby non-interacting particles following a period of diffusion. We propose the use of…
Spectral properties of random matrices play an important role in statistics, machine learning, communications, and many other areas. Engaging results regarding the convergence of the empirical spectral distribution (ESD) and the…
A statistical analysis of the prime numbers indicates possible traces of quantum chaos. We have computed the nearest neighbor spacing distribution, number variance, skewness, and excess for sequences of the first N primes for various values…
We theoretically study propagating correlation fronts in non-interacting fermions on a one-dimensional lattice starting from an alternating state, where the fermions occupy every other site. We find that, in the long-time asymptotic regime,…
Quantum chaotic systems with one-dimensional spectra follow spectral correlations of orthogonal (OE), unitary (UE), or symplectic ensembles (SE) of random matrices depending on their invariance under time reversal and rotation. In this…
We study the distribution of entries of a random permutation matrix under a "randomized basis," i.e., we conjugate the random permutation matrix by an independent random orthogonal matrix drawn from Haar measure. It is shown that under…
We study the effects of uniform time delays on the extreme fluctuations in stochastic synchronization and coordination problems with linear couplings in complex networks. We obtain the average size of the fluctuations at the nodes from the…
A statistical analysis of the spectrum of two particle - two hole doorway states in a finite nucleus is performed. On the unperturbed mean-field level sizable attractive correlations are present in such a spectrum. Including particle-hole…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
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 measured the ensemble-averaged spectral correlation functions and statistical distributions of spectral spacing and intensity for lasing modes in weakly scattering systems, and compared them to those of the amplified spontaneous emission…
Motivated by the hyperfine interaction of electron spins with surrounding nuclei, we investigate systems of central spins coupled to a bath of noninteracting spins in the framework of random matrix theory. With increasing number of central…
We extend the results about the fluctuations of the matrix entries of regular functions of Wigner matrices to the case of sample covariance random matrices.
We study a class of interacting particle systems on $\mathbb{R}$ which was recently investigated by F. G\"otze and the second author [GV14]. These ensembles generalize eigenvalue ensembles of Hermitian random matrices by allowing different…
In an earlier work we had considered a Gaussian ensemble of random matrices in the presence of a given external matrix source. The measure is no longer unitary invariant and the usual techniques based on orthogonal polynomials, or on the…
We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…
We investigate the relationship between information scrambling and work statistics after a quench for the paradigmatic example of short-range interacting particles in a one-dimensional harmonic trap, considering up to five particles…
We introduce the theater model, which is the simplest variant of directed random sequential adsorption in one dimension with point source and steric interactions. Particles enter sequentially an initially empty row of $L$ sites and adsorb…
It recently has been found that methods of the statistical theories of spectra can be a useful tool in the analysis of spectra far from levels of Hamiltonian systems. Several examples originate from areas, such as quantitative linguistics…