Related papers: Hidden Breit-Wigner distribution and other propert…
For two interacting particles (TIP) in one-dimensional random potential the dependence of the Breit-Wigner width $\Gamma$, the local density of states and the TIP localization length on system parameters is determined analytically. The…
Random banded matrices with linearly increasing diagonal elements are recently considered as an attractive model for complex nuclei and atoms. Apart from early papers by Wigner \cite{Wig} there were no analytical studies on the subject. In…
We analytically calculate the local density of states for Cauchy random band matrices with strongly fluctuating diagonal elements. The Breit-Wigner form for ordinary band matrices is replaced by a Levy distribution of index $\mu=1/2$ and…
It is shown that, for a Hamiltonian with a band structure, the half width of local spectral density of states, or strength function, is closely related to the width of the nonperturbative (NPT) parts of energy eigenfunctions. In the…
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…
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 derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced to study spectral properties of many-body…
We study the statistical properties of eigenvalues of the Hessian matrix ${\cal H}$ (matrix of second derivatives of the potential energy) for a classical atomic liquid, and compare these properties with predictions for random matrix models…
Although the spectra of random networks have been studied for a long time, the influence of network topology on the dense limit of network spectra remains poorly understood. By considering the configuration model of networks with four…
We survey recent mathematical results about the spectrum of random band matrices. We start by exposing the Erd{\H o}s-Schlein-Yau dynamic approach, its application to Wigner matrices, and extension to other mean-field models. We then…
We consider the empirical eigenvalue distribution of random real symmetric matrices with stochastically independent skew-diagonals and study its limit if the matrix size tends to infinity. We allow correlations between entries on the same…
We study the properties of the discrete Wigner distribution for two qubits introduced by Wotters. In particular, we analyze the entanglement properties within the Wigner distribution picture by considering the negativity of the Wigner…
Using the supersymmetry method we analytically calculate the local density of states, the localiztion length, the generalized inverse participation ratios, and the distribution function of eigenvector components for the superposition of a…
The scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semi-circular distribution, has attracted much attention. The $2k$th moment of the limit equals…
We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such…
We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is…
In these notes we review recent progress (and, in Section \ref{sec:ados}, we announce a new result) concerning the statistical properties of the spectrum of Wigner random matrices.
We consider a class of random banded Hessenberg matrices with independent entries having identical distributions along diagonals. The distributions may be different for entries belonging to different diagonals. For a sequence of $n\times n$…
We investigate spectral properties of a discrete random displacement model, a Schr\"odinger operator on $\ell^2(\Z^d)$ with potential generated by randomly displacing finitely supported single-site terms from the points of a sublattice of…
The paper studies the spectral properties of large Wigner, band and sample covariance random matrices with heavy tails of the marginal distributions of matrix entries.