Related papers: Sparse random matrix configurations for two or thr…
We analyze the spectral distribution of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independent, the elements of the diagonals are taken to be correlated.…
Given a matrix A \in R^{m x n}, we present a randomized algorithm that sparsifies A by retaining some of its elements by sampling them according to a distribution that depends on both the square and the absolute value of the entries. We…
Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of…
Quantum systems are often described by parameter-dependent Hamiltonians. Points in parameter space where two levels are degenerate can carry a topological charge. Here we theoretically study an interacting two-spin system where the…
We investigate the low-lying spectra of many-body systems with random two-body interactions, specifying that the ensemble be invariant under particle-hole conjugation.Surprisingly we find patterns reminiscent of more orderly interactions,…
We study the behavior of exponential random graphs in both the sparse and the dense regime. We show that exponential random graphs are approximate mixtures of graphs with independent edges whose probability matrices are critical points of…
We consider one-dimensional asymmetric exclusion processes with a simple attractive interaction, where the distance between consecutive particles is not allowed to exceed a certain limit and investigate the consequences of this coupling on…
We study spectral behavior of sparsely connected random networks under the random matrix framework. Sub-networks without any connection among them form a network having perfect community structure. As connections among the sub-networks are…
We investigate the spectral distribution of random matrix ensembles with correlated entries. We consider symmetric matrices with real valued entries and stochastically independent diagonals. Along the diagonals the entries may be…
We study a three-body system with zero-range interactions in a one-dimensional harmonic trap. The system consists of two spin-polarized fermions and a third particle which is distinct from two others (2+1 system). First we assume that the…
Theoretical analysis of biological and artificial neural networks e.g. modelling of synaptic or weight matrices necessitate consideration of the generic real-asymmetric matrix ensembles, those with varying order of matrix elements e.g. a…
Statistical distribution of energy levels for Dirac fermions confined in a quantum dot is studied numerically on the examples of triangular and hexagonal graphene flakes with random electrostatic potential landscape. When increasing the…
We study a two-dimensional system of two Coulombically interacting electrons in an external harmonic confining potential. More precisely, we present calculations for the singlet ground-state of the system. We explain the nature of the…
We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined…
We study the interlayer pairing states in layered systems of two different 2d electronic subsystems, one with relativistic linear and the other with non-relativistic parabolic spectrum. The complex order parameter of the paired state has a…
Two families of strongly non-Gaussian random matrix ensembles (RME) are considered. They are statistically equivalent to a one-dimensional plasma of particles interacting logarithmically and confined by the potential that has the long-range…
We propose a one-dimensional nonintegrable spin model with local interactions that covers Dyson's three symmetry classes (classes A, AI, and AII) depending on the values of parameters. We show that the nearest-neighbor spacing distribution…
We consider the frequency at which avoided crossings appear in an energy level structure when an external field is applied to a quantum chaotic system. The distribution of the spacing in the parameter between two adjacent avoided crossings…
We consider the problem of recovering an unknown low-rank matrix X with (possibly) non-orthogonal, effectively sparse rank-1 decomposition from measurements y gathered in a linear measurement process A. We propose a variational formulation…
We study the limiting behavior of interacting particle systems indexed by large sparse graphs, which evolve either according to a discrete time Markov chain or a diffusion, in which particles interact directly only with their nearest…