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We have calculated the joint probability distribution function for random reverse-cyclic matrices and shown that it is related to an N-body exactly solvable model. We refer to this well-known model potential as a screened harmonic…
The power-law random banded matrices and the ultrametric random matrices are investigated numerically in the regime where eigenstates are extended but all integer matrix moments remain finite in the limit of large matrix dimensions. Though…
Statistical properties of ensembles of random density matrices are investigated. We compute traces and von Neumann entropies averaged over ensembles of random density matrices distributed according to the Bures measure. The eigenvalues of…
We consider the spectral statistics of large random band matrices on mesoscopic energy scales. We show that the two-point correlation function of the local eigenvalue density exhibits a universal power law behaviour that differs from the…
Kinetic simulations of relativistic turbulence have significantly advanced our understanding of turbulent particle acceleration. Recent progress has highlighted the need for an updated acceleration theory that can account for acceleration…
We study the structure of eigenstates in two-body interaction random matrix ensembles and find significant deviations from random matrix theory expectations. The deviations are most prominent in the tails of the spectral density and…
We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
We call a multidimensional distribution to be decomposable with respect to a partition of two sets of coordinates if the original distribution is the product of the marginal distributions associated with these two sets. We focus on the…
We establish an equivalence between two classes of methods for solving fractional diffusion problems, namely, Reduced Basis Methods (RBM) and Rational Krylov Methods (RKM). In particular, we demonstrate that several recently proposed RBMs…
For random matrix ensembles with non-gaussian matrix elements that may exhibit some correlations, it is shown that centered traces of polynomials in the matrix converge in distribution to a Gaussian process whose covariance matrix is…
Optical beam propagation in random media is characterized by familiar speckle patterns generated by intricate interference effects. Such patterns may be modified and possibly attenuated for partially coherent incident beam profiles. In the…
We present a semiclassical approach to eigenfunction statistics in chaotic and weakly disordered quantum systems which goes beyond Random Matrix Theory, supersymmetry techniques, and existing semiclassical methods. The approach is based on…
Spectral properties of Hermitian Toeplitz, Hankel, and Toeplitz-plus-Hankel random matrices with independent identically distributed entries are investigated. Combining numerical and analytic arguments it is demonstrated that spectral…
Linear electromagnetic wave scattering systems can be characterized by an impedance matrix that relates the voltages and currents at the ports of the system. When the system size becomes greater than the wavelength of the fields involved,…
Random matrix models based on an integral over supermatrices are proposed as a natural extension of bosonic matrix models. The subtle nature of superspace integration allows these models to have very different properties from the analogous…
We have calculated wave functions and matrix elements of the dipole operator in the two- and three-dimensional Anderson model of localization and have studied their statistical properties in the limit of weak disorder. In particular, we…
Graphical models are a rich language for describing high-dimensional distributions in terms of their dependence structure. While there are algorithms with provable guarantees for learning undirected graphical models in a variety of…
The Probability Distribution Function of plasma density fluctuations at the edge of fusion devices is known to be skewed and strongly non-Gaussian. The causes of this peculiar behaviour are, up to now, largely unexplored. On the other hand,…
We investigate spectral fluctuations in multilayer networks within the random matrix theory (RMT) framework to characterize universal and non-universal features. The adjacency matrix of a multilayer network exhibits a block structure, with…