Related papers: Perturbation theory for Hermitian matrix-functions…
We construct higher order spectral shift functions, which represent the remainders of Taylor-type approximations for the value of a function at a perturbed self-adjoint operator by derivatives of the function at an initial unbounded…
We study the spectral tilt of primordial perturbations in Horava-Lifshitz cosmology. The uniform approximation, which is a generalization of the familiar Wentzel-Kramers-Brillouin (WKB) method, is employed to compute the spectral index both…
We estimate the size of the spectral gap at zero for some Hermitian block matrices. Included are quasi-definite matrices, quasi-semidefinite matrices (the closure of the set of the quasi-definite matrices) and some related block matrices…
A remarkable mathematical property -- somehow hidden and recently rediscovered -- allows obtaining the eigenvectors of a Hermitian matrix directly from their eigenvalues. That opens the possibility to get the wavefunctions from the…
We study the convergence of sequences of type I and type II Hermite-Pad\'e approximants for certain systems of meromorphic functions made up of rational modifications of Nikishin systems of functions.
The paper deals with (multidimensional and one-dimensional) Bochner-Phillips functional calculus. Bounded perturbations of Bernstein functions of (one or several commuting) semigroup generators on Banach spaces are considered, conditions…
Let $\mathcal{L}$ be the special Hermite operator on $\mathbb{C}^n$. As a continuation of the recent results in \cite{SG}, we establish new Strichartz estimates for systems of orthonormal functions associated with general flows of the form…
This paper considers random (non-Hermitian) circulant matrices, and proves several results analogous to recent theorems on non-Hermitian random matrices with independent entries. In particular, the limiting spectral distribution of a random…
The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Determinantal formulas, relation to conformal field models and the theory of Generalized Kontsevich model are discussed in some…
We review the status and present range of applications of the ``string-inspired'' approach to perturbative quantum field theory. This formalism offers the possibility of computing effective actions and S-matrix elements in a way which is…
Eigenvalue and eigenvector perturbation theory is a fundamental topic in several disciplines, including numerical linear algebra, quantum physics, and related fields. The central problem is to understand how the eigenvalues and eigenvectors…
We consider $n\times n$ non-Hermitian random matrices with independent entries and a variance profile, as well as an additive deterministic diagonal deformation. We show that their empirical eigenvalue distribution converges to a limiting…
A new formulation of four dimensional quantum field theories, such as scalar field theory, is proposed as a large N limit of a special NxN matrix model. Our reduction scheme works beyond planar approximation and applies for QFT with finite…
A spectral approach to building the exterior calculus in manifold learning problems is developed. The spectral approach is shown to converge to the true exterior calculus in the limit of large data. Simultaneously, the spectral approach…
The spectrum of primordial fluctuations from inflation can be obtained using a mathematically controlled, and systematically extendable, uniform approximation. Closed-form expressions for power spectra and spectral indices may be found…
In this paper we derive sequences of Gershgorin-type inclusion sets for the spectra and pseudospectra of finite matrices. In common with previous generalisations of the classical Gershgorin bound for the spectrum, our inclusion sets are…
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 draw attention to the fact that a Hermitian matrix is always diagonalizable and has real discrete spectrum whereas the Hermitian Schr{\"o}dinger Hamiltonian: $H=p^2/2\mu+V(x)$, may not be so. For instance when $V(x)=x, x^3, -x^2$, $H$…
In this paper, we apply ideas of Dijkgraaf and Witten on 2+1 dimensional topological quantum field theory to arithmetic curves, that is, the spectra of rings of integers in algebraic number fields. In the first three sections, we define…
A new totally algebraic formalism based on general, abstract ladder operators has been proposed. This approach heavily grounds in the superoperator formalism of Primas. However it is necessary to introduce many improvements in his…