Related papers: Eigenvalue distribution of canonical systems: trac…
We investigate the universality of singular value and eigenvalue distributions of matrix valued functions of independent random matrices and apply these general results in several examples. In particular we determine the limit distribution…
We investigate the fluctuations around the mean of the Stieltjes transform of the empirical spectral distribution of any selfadjoint noncommutative polynomial in a Wigner matrix and a deterministic diagonal matrix. We obtain the convergence…
The computation of eigenvalues of large-scale matrices arising from finite element discretizations has gained significant interest in the last decade. Here we present a new algorithm based on slicing the spectrum that takes advantage of the…
We study the minimum of the essential spectrum of canonical systems $Ju'=-zHu$. Our results can be described as a generalized and more quantitative version of the characterization of systems with purely discrete spectrum, which was recently…
Scattering resonances arise in wave phenomena and play an important role in many applications. While extensive theoretical studies have been conducted, effective numerical computation remains limited, and most existing methods suffer from…
We study the dynamics of the entanglement spectrum, that is the time evolution of the eigenvalues of the reduced density matrices after a bipartition of a one-dimensional spin chain. Starting from the ground state of an initial Hamiltonian,…
An equation is obtained for the Stieltjes transform of the normalized distribution of singular values of non-symmetric band random matrices in the limit when the band width and rank of the matrix simultaneously tend to infinity. Conditions…
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…
An original approach to the inverse scattering for Jacobi matrices was suggested in a recent paper by Volberg-Yuditskii. The authors considered quite sophisticated spectral sets (including Cantor sets of positive Lebesgue measure), however…
For a large class of linear neutral type systems the problem of eigenvalues and eigenvectors assignment is investigated, i.e. finding the system which has the given spectrum and almost all, in some sense, eigenvectors.
In this article, we study microscopic properties of a two-dimensional eigenvalue ensemble near a conical singularity arising from insertion of a point charge in the bulk of the support of eigenvalues. In particular, we characterize all…
We introduce and analyse ensembles of 2-regular random graphs with a tuneable distribution of short cycles. The phenomenology of these graphs depends critically on the scaling of the ensembles' control parameters relative to the number of…
We discuss a method of the asymptotic computation of moments of the normalized eigenvalue counting measure of random matrices of large order. The method is based on the resolvent identity and on some formulas relating expectations of…
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 present a method of cones for rigorous estimations of eigenvectors, eigenspaces and eigenvalues of a matrix. The key notion is the cone-domination and is inspired by ideas from hyperbolic dynamical systems. We present theorems which…
We consider ensembles of Wigner matrices, whose entries are (up to the symmetry constraints) independent and identically distributed random variables. We show the convergence of the Stieltjes transform towards the Stieltjes transform of the…
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 revisit the derivation of the density of states of sparse random matrices. We derive a recursion relation that allows one to compute the spectrum of the matrix of incidence for finite trees that determines completely the low…
A canonical system is a kind of first-order system of ordinary differential equations on an interval of the real line parametrized by complex numbers. It is known that any solution of a canonical system generates an entire function of the…
A two-dimensional Schr\"odinger operator with a constant magnetic field perturbed by a smooth compactly supported potential is considered. The spectrum of this operator consists of eigenvalues which accumulate to the Landau levels. We call…