Related papers: Exact spectral densities of complex noise-plus-str…
We study the statistical and dynamic properties of the systems characterized by an ultrametric space of states and translationary non-invariant symmetric transition matrices of the Parisi type subjected to "locally constant" randomization.…
In many applications it is important to understand the sensitivity of eigenvalues of a matrix polynomial to perturbations of the polynomial. The sensitivity commonly is described by condition numbers or pseudospectra. However, the…
The density of complex eigenvalues of random asymmetric $N\times N$ matrices is found in the large-$N$ limit. The matrices are of the form $H_0+A$ where $A$ is a matrix of $N^2$ independent, identically distributed random variables with…
We study the spectral density of factor models of multivariate time series. By making use of the Random Matrix Theory we analytically quantify the effect of noise dressing on the spectral density due to the finiteness of the sample. We…
Consider large signal-plus-noise data matrices of the form $S + \Sigma^{1/2} X$, where $S$ is a low-rank deterministic signal matrix and the noise covariance matrix $\Sigma$ can be anisotropic. We establish the asymptotic joint distribution…
A statistical description of part of a many body system often requires a non-Hermitian random matrix ensemble with nature and strength of randomness sensitive to underlying system conditions. For the ensemble to be a good description of the…
We present a general framework for inverse design of nanopatterned surfaces that maximize spatially averaged surface-enhanced Raman (SERS) spectra from molecules distributed randomly throughout a material or fluid, building upon a recently…
We consider the reduced density matrix of a large block of consecutive spins in the ground states of the XY spin chain on an infinite lattice. We derive the spectrum of the density matrix using the expression of the Renyi entropy in terms…
We discuss the limiting spectral density of real symmetric random matrices. Other than in standard random matrix theory the upper diagonal entries are not assumed to be independent, but we will fill them with the entries of a stochastic…
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…
We provide a detailed derivation of the spectral density of the stochastic background generated by the superposition of coalescing compact binaries. We show how the expression often used in the literature emerges from an average over the…
We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module connectivity is taken to be incomplete.…
Imaging of perfectly conducting crack(s) in a 2-D homogeneous medium using boundary data is studied. Based on the singular structure of the Multi-Static Response (MSR) matrix whose elements are normalized by an adequate test function at…
We consider the additive superimposition of an extensive number of independent Euclidean Random Matrices in the high-density regime. The resolvent is computed with techniques from free probability theory, as well as with the replica method…
Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…
We consider a versatile matrix model of the form ${\bf A}+i {\bf B}$, where ${\bf A}$ and ${\bf B}$ are real random circulant matrices with independent but, in general, nonidentically distributed Gaussian entries. For this model, we derive…
In order to clarify the statistical features of complex networks, the spectral density of adjacency matrices has often been investigated. Adopting a static model introduced by Goh, Kahng and Kim, we analyse the spectral density of complex…
We consider the ensemble of $N\times N$ ($N\gg 1$) symmetric random matrices with the bimodal independent distribution of matrix elements: each element could be either "1" with the probability $p$, or "0" otherwise. We pay attention to the…
In this work, we consider the weighted difference of two independent complex Wishart matrices and derive the joint probability density function of the corresponding eigenvalues in a finite-dimension scenario using two distinct approaches.…
We compute the spectral statistics of the sum H of two independent complex Wishart matrices, each of which is correlated with a different covariance matrix. Random matrix theory enjoys many applications including sums and products of random…