相关论文: Spectral density in a Moszynski's class of Jacobi …
We consider a new class of non-self-adjoint matrices that arise from an indefinite self-adjoint linear pencil of matrices, and obtain the spectral asymptotics of the spectra as the size of the matrices diverges to infinity. We prove that…
Exposed positive maps in matrix algebras define a dense subset of extremal maps. We provide a sufficient condition for a positive map to be exposed. This is an analog of a spanning property which guaranties that a positive map is optimal.…
In hep-th/0111281 the complete set of eigenvectors and eigenvalues of Neumann matrices was found. It was shown also that the spectral density contains a divergent constant piece that being regulated by truncation at level L equals (log…
We use supersymmetry to calculate exact spectral densities for a class of complex random matrix models having the form $M=S+LXR$, where $X$ is a random noise part $X$ and $S,L,R$ are fixed structure parts. This is a certain version of the…
We investigate combinatorial properties of aperiodic simple Toeplitz subshifts, as well as spectral properties of Jacobi operators defined by them. More precisely, we derive explicit formulas for complexity, palindrome complexity and, for…
The generic linear evolution of the density matrix of a system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. These dynamical stochastic maps form a linear…
We prove that Jacobi, CMV, and Schr\"odinger operators, which are reflectionless on a homogeneous set E (in the sense of Carleson), under the assumption of a Blaschke-type condition on their discrete spectra accumulating at E, have purely…
It is shown generally that any oscillation probability in matter with approximately constant density coincides with that in vacuum to the first two nontrivial orders in $\Delta m^2_{jk}L/E$ if $|\Delta m^2_{jk}L/E|\ll 1$ and $|G_F N_e L|\ll…
We study the spectral theory of a class of piecewise centrosymmetric Jacobi operators defined on an associated family of substitution graphs. Given a finite centrosymmetric matrix viewed as a weight matrix on a finite directed path graph…
Jacobi matrices probably are the most classical object in spectral theory, while CMV matrices are a comparably fresh one, although they are related to a very classical topic, namely to orhtogonal polynomials on the unit circle (in the same…
Covariance matrix of heights measured relative to the average height of a growing self-affine surface in the steady state are investigated in the framework of random matrix theory. We show that the spectral density of the covariance matrix…
We study the complex spectrum of the partial theta function \[ \Theta(q,x)=\sum_{j=0}^{\infty}q^{j(j+1)/2}x^j, \qquad |q|<1, \] where a spectral value is a parameter for which \(\Theta(q,\cdot)\) has a multiple zero. Since the function is…
We show that an intensity speckle can be directly interpreted as the properties of incident light - amplitude, phase, polarization, and coherency over spatial positions. Revisiting the speckle-correlation scattering matrix (SSM) method [Lee…
We consider matrices on infinite trees which are universal covers of Jacobi matrices on finite graphs. We are interested in the question of the existence of sequences of finite covers whose normalized eigenvalue counting measures converge…
We introduce, in the dual Macaev ideal of compact operators of a Hilbert space, the spectral weight $\rho(L)$ of a positive, self-adjoint operator $L$ having discrete spectrum away from zero. We provide criteria for its measurability and…
We give a simple and explicit description of the Bernstein-Szego type measures associated with Jacobi matrices which differ from the Jacobi matrix of the Chebyshev measure in finitely many entries. We also introduce a class of measures M…
A regular map is a surface together with an embedded graph, having properties similar to those of the surface and graph of a platonic solid. We analyze regular maps with reflection symmetry and a graph of density strictly exceeding 1/2, and…
One of the first theorems in perturbation theory claims that for an arbitrary self-adjoint operator A there exists a perturbation B of Hilbert-Schmidt class, which destroys completely the absolutely continuous spectrum of A (von Neumann).…
We show that the space of expanding maps contains an open and dense set where smooth conjugacy classes of expanding maps are determined by the values of the Jacobians of return maps at periodic points.
In this note we study the entropy spectrum of rotation classes for collections of finitely many continuous potentials $\varphi_1,\dots,\varphi_m:X\to \mathbb{R}$ with respect to the set of invariant measures of an underlying dynamical…