Related papers: Analytical Results for Random Band Matrices with P…
We study statistical properties of the ensemble of large $N\times N$ random matrices whose entries $ H_{ij}$ decrease in a power-law fashion $H_{ij}\sim|i-j|^{-\alpha}$. Mapping the problem onto a nonlinear $\sigma-$model with non-local…
Reconstructing a density of states or similar distribution from moments or continued fractions is an important problem in calculating the electronic and vibrational structure of defective or non-crystalline solids. For single bands a…
The density band model proposed by Kassam for robust hypothesis testing is revisited in this paper. First, a novel criterion for the general characterization of least favorable distributions is proposed, which unifies existing results. This…
This paper develops a general asymptotic theory of local polynomial (LP) regression for spatial data observed at irregularly spaced locations in a sampling region $R_n \subset \mathbb{R}^d$. We adopt a stochastic sampling design that can…
Consider an $ N \times N$ Hermitian one-dimensional random band matrix with band width $W > N^{1 / 2 + \frak c} $ for any $ {\frak c} > 0$. In the bulk of the spectrum and in the large $ N $ limit, we obtain the following results: (i) The…
The probability distribution of the reflection coefficient for light reflected from a one-dimensional random amplifying medium with {\it cross-correlated} spatial disorder in the real and the imaginary parts of the refractive index is…
We consider a dynamics generated by families of maps whose invariant density depends on a parameter a and where a itself obeys a stochastic or periodic dynamics. For slowly varying a the long-term behavior of iterates is described by a…
This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…
We discuss the concept of connection states (or connection matrices) that describe posterior ensembles, post-selected according to the outcomes of a quantum measurement. Connection matrices allow one to obtain results of any weak and some…
We study Hermitian random matrix models with an external source matrix which has equispaced eigenvalues, and with an external field such that the limiting mean density of eigenvalues is supported on a single interval as the dimension tends…
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…
One of the major themes of random matrix theory is that many asymptotic properties of traditionally studied distributions of random matrices are universal. We probe the edges of universality by studying the spectral properties of random…
Applying the replica method of statistical mechanics, we evaluate the eigenvalue density of the large random matrix (sample covariance matrix) of the form $J = A^{\rm T} A$, where $A$ is an $M \times N$ real sparse random matrix. The…
A theoretical analysis of the statistical distributions of the reflected intensities from random media is presented. We use random matrix theory to analytically deduce the probability densities in the localization regime. Numerical…
We show the density of eigenvalues for three classes of random matrix ensembles is determinantal. First we derive the density of eigenvalues of product of $k$ independent $n\times n$ matrices with i.i.d. complex Gaussian entries with a few…
The spectral and localization properties of heterogeneous random graphs are determined by the resolvent distributional equations, which have so far resisted an analytic treatment. We solve analytically the resolvent equations of random…
Inspired by works on the Anderson model on sparse graphs, we devise a method to analyze the localization properties of sparse systems that may be solved using cavity theory. We apply this method to study the properties of the eigenvectors…
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…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
We consider the Gaussian ensembles of random matrices and describe the normal modes of the eigenvalue spectrum, i.e., the correlated fluctuations of eigenvalues about their most probable values. The associated normal mode spectrum is…