Related papers: Eigenvalue Repulsion and Eigenfunction Localizatio…
We explore the spectra and localization properties of the N-site banded one-dimensional non-Hermitian random matrices that arise naturally in sparse neural networks. Approximately equal numbers of random excitatory and inhibitory…
Sparse non-Hermitian random matrices arise in the study of disordered physical systems with asymmetric local interactions, and have applications ranging from neural networks to ecosystem dynamics. The spectral characteristics of these…
Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction…
We consider a discrete, non-Hermitian random matrix model, which can be expressed as a shift of a rank-one perturbation of an anti-symmetric matrix. We show that, asymptotically almost surely, the real parts of the eigenvalues of the…
This work shows that dynamical features typical of full random matrices can be observed also in the simple finite one-dimensional (1D) noninteracting Anderson model with nearest neighbor couplings. In the thermodynamic limit, all…
Eigenvalues statistics of various many-body systems have been widely studied using the nearest neighbor spacing distribution under the random matrix theory framework. Here, we numerically analyze eigenvalue ratio statistics of multiplex…
This paper examines the relationship between sparse random network architectures and neural network stability by examining the eigenvalue spectral distribution. Specifically, we generalise classical eigenspectral results to sparse…
We explore the concept of eigenvalue avoidance, which is well understood for real symmetric and Hermitian matrices, for other classes of structured matrices. We adopt a differential geometric perspective and study the generic behaviour of…
We study spectra of directed networks with inhibitory and excitatory couplings. We investigate in particular eigenvector localization properties of various model networks for different value of correlation among their entries. Spectra of…
Symmetries associated with complex conjugation and Hermitian conjugation, such as time-reversal symmetry and pseudo-Hermiticity, have great impact on eigenvalue spectra of non-Hermitian random matrices. Here, we show that time-reversal…
The dynamics of non-Hermitian quantum systems have taken on an increasing relevance in light of quantum devices which are not perfectly isolated from their environment. The interest in them also stems from their fundamental differences from…
We study the transport and spectral properties of a non-Hermitian one-dimensional disordered lattice, the diagonal matrix elements of which are random complex variables taking both positive (loss) and negative (gain) imaginary values: Their…
We develop a theory which describes the behaviour of eigenvalues of a class of one-dimensional random non-Hermitian operators introduced recently by Hatano and Nelson. Under general assumptions on random parameters we prove that the…
We propose a technique for calculating and understanding the eigenvalue distribution of sums of random matrices from the known distribution of the summands. The exact problem is formidably hard. One extreme approximation to the true density…
Spectra of sparse non-Hermitian random matrices determine the dynamics of complex processes on graphs. Eigenvalue outliers in the spectrum are of particular interest, since they determine the stationary state and the stability of dynamical…
We compute analytically the joint probability density of eigenvalues and the level spacing statistics for an ensemble of random matrices with interesting features. It is invariant under the standard symmetry groups (orthogonal and unitary)…
We study local correlations of certain interacting particle systems on the real line which show repulsion similar to eigenvalues of random Hermitian matrices. Although the new particle system does not seem to have a natural spectral or…
It has been observed that the statistical distribution of the eigenvalues of random matrices possesses universal properties, independent of the probability law of the stochastic matrix. In this article we find the correlation functions of…
Within the framework of non-Hermitian photonics, we investigate the spectral and dynamical properties of one- and two-dimensional non-Hermitian off-diagonal disordered optical lattices, where randomness is applied to the couplings rather…
Models of disorder with a direction (constant imaginary vector-potential) are considered. These non-Hermitian models can appear as a result of computation for models of statistical physics using transfer matrix technique or describe…