Related papers: Eigenvalues of Symmetric Non-normalized Discrete T…
This is the first in a series of papers addressing the phenomenon of dimensional transmutation in nonrelativistic quantum mechanics within the framework of dimensional regularization. Scale-invariant potentials are identified and their…
We obtain the asymptotic distribution of eigenvalues of real symmetric tridiagonal matrices as their dimension increases to infinity and whose diagonal and off-diagonal elements asymptotically change with the index n as J_{nt+i nt+i}\sim…
Second order nonlinear eigenvalue problems are considered for which the spectrum is an interval. The boundary conditions are of Robin and Dirichlet type. The shape and the number of solutions are discussed by means of a phase plane…
We revisit 6d (2,0) SCFTs of type $D_N$ and their realization in M-theory, focusing on absolute variants of these theories and on their global finite 0- and 2-form symmetries. We derive the 7d SymTFT capturing these global symmetries from…
We give two characterization theorems for pseudo-Hermitian (possibly nondiagonalizable) Hamiltonians with a discrete spectrum that admit a block-diagonalization with finite-dimensional diagonal blocks. In particular, we prove that for such…
In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…
Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and…
Given a non-hermitean matrix M, the structure of its minimal polynomial encodes whether M is diagonalizable or not. This note will explain how to determine the minimal polynomial of a matrix without going through its characteristic…
There has been much recent interest, initiated by work of the physicists Hatano and Nelson, in the eigenvalues of certain random non-Hermitian periodic tridiagonal matrices and their bidiagonal limits. These eigenvalues cluster along a…
This paper is concerned with the interplay between statistical asymmetry and spectral methods. Suppose we are interested in estimating a rank-1 and symmetric matrix $\mathbf{M}^{\star}\in \mathbb{R}^{n\times n}$, yet only a randomly…
In this work, we introduce a definition of the Discrete Fourier Transform (DFT) on Euclidean lattices in $\R^n$, that generalizes the $n$-th fold DFT of the integer lattice $\Z^n$ to arbitrary lattices. This definition is not applicable for…
We consider a product of an arbitrary number of independent rectangular Gaussian random matrices. We derive the mean densities of its eigenvalues and singular values in the thermodynamic limit, eventually verified numerically. These…
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…
Differential geometric approaches to the analysis and processing of data in the form of symmetric positive definite (SPD) matrices have had notable successful applications to numerous fields including computer vision, medical imaging, and…
The eigenvalue spectrum of the transition matrix of a network encodes important information about its structural and dynamical properties. We study the transition matrix of a family of fractal scale-free networks and analytically determine…
This paper is a detailed account of the recent progress in understanding the statistical properties of complex eigenvalues of random non-Hermitian matrices reported earlier in our two short communications: Physics Letters A v.226, 46 (1997)…
This summary of the doctoral thesis provides a comprehensive formulation of the Extended Discrete Fourier Transform (EDFT), derived directly from the Fourier integral and its orthogonality properties. The method is obtained by solving…
This paper investigates finite-dimensional representations of PT-symmetric Hamiltonians. In doing so, it clarifies some of the claims made in earlier papers on PT-symmetric quantum mechanics. In particular, it is shown here that there are…
We introduce a new biharmonic Steklov problem on differential forms with Dirichlet-type boundary conditions and show that it is elliptic. We prove the existence of a discrete spectrum for this problem and give variational characterizations…
We show that the authors of the commented paper draw their conclusions from the eigenvalues of truncated Hamiltonian matrices that do not converge as the matrix dimension increases. In one of the studied examples the authors missed the real…