Related papers: Matrices coupled in a chain. I. Eigenvalue correla…
The product of a Hermitian matrix and a positive semidefinite matrix has only real eigenvalues. We present bounds for sums of eigenvalues of such a product.
Our interest is in the scaled joint distribution associated with $k$-increasing subsequences for random involutions with a prescribed number of fixed points. We proceed by specifying in terms of correlation functions the same distribution…
Symmetrizable matrices are those which are symmetric when multiplied by a diagonal matrix with positive entries. The Cauchy interlace theorem states that the eigenvalues of a real symmetric matrix interlace with those of any principal…
Correlations of eigenfunctions, $\langle|\psi_k(r_1)|^2|\psi_l(r_2)|^2\rangle$, in a disordered system are investigated. We derive general formulae expressing these correlation functions in terms of the supermatrix sigma-model. In…
We study a general class of recurrence relations that appear in the application of a matrix diagonalization procedure. We find general closed formula and determine analytical properties of the solutions. We finally apply these findings in…
We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson…
We obtain the time-dependent correlation function describing the evolution of a single spin excitation state in a linear spin chain with isotropic nearest-neighbour XY coupling, where the Hamiltonian is related to the Jacobi matrix of a set…
For a given complex square matrix $A$ with constant row sum, we establish two new eigenvalue inclusion sets. Using these bounds, first we derive bounds for the second largest and smallest eigenvalues of adjacency matrices of $k$-regular…
We describe Generalized Hermitian matrices ensemble sometimes called Chiral ensemble. We give global asymptotic of the density of eigenvalues or the statistical density. We will calculate a Laplace transform of such a density for finite…
We extend Carleson's interpolation Theorem to sequences of matrices, by giving necessary and sufficient separation conditions for a sequence of matrices to be interpolating.
A truncation of a Haar distributed orthogonal random matrix gives rise to a matrix whose eigenvalues are either real or complex conjugate pairs, and are supported within the closed unit disk. This is also true for a product $P_m$ of $m$…
We develop a general theory for Markov chains whose transition probabilities are the coefficients of descent operators on combinatorial Hopf algebras. These model the breaking-then-recombining of combinational objects. Examples include the…
Many real world systems can be expressed as complex networks of interconnected nodes. It is frequently important to be able to quantify the relative importance of the various nodes in the network, a task accomplished by defining some…
Matrix integrals used in random matrix theory for the study of eigenvalues of Hermitian ensembles have been shown to provide $\tau$-functions for several hierarchies of integrable equations. In this article, we extend this relation by…
We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by…
A superposition of a matrix ensemble refers to the ensemble constructed from two independent copies of the original, while a decimation refers to the formation of a new ensemble by observing only every second eigenvalue. In the cases of the…
It is well known that the set of all $ n \times n $ matrices with distinct eigenvalues is a dense subset of the set of all real or complex $ n \times n $ matrices. In [Hartfiel, D. J. Dense sets of diagonalizable matrices. Proc. Amer. Math.…
We obtain generalisations of some inequalities for positive unital linear maps on matrix algebra. This also provides several positive semidefinite matrices and we get some old and new inequalities involving the eigenvalues of a Hermitian…
We derive a general Hamiltonian that governs the interaction between an $N$-ion chain and an externally controlled laser field, where the ion motion is quantized and the laser field is considered beyond the plane-wave approximation. This…
This study presents a generalization for a method examining the correlation function of an arbitrary system with interactions in an Ising model to obtain a value of correlation between two arbitrary points on a network. The establishment of…