Related papers: Derivative principles for invariant ensembles
We consider $N\times N$ Hermitian or symmetric random matrices with independent entries. The distribution of the $(i,j)$-th matrix element is given by a probability measure $\nu_{ij}$ whose first two moments coincide with those of the…
We consider the problem of writing real polynomials as determinants of symmetric linear matrix polynomials. This problem of algebraic geometry, whose roots go back to the nineteenth century, has recently received new attention from the…
In this paper, a new identity for differentiable functions is derived. A consequence of the identity is that the author establishes some new general inequalities containing all of the Hermite-Hadamard and Simpson-like type for functions…
The spectral theory for operator pencils and operator differential-algebraic equations is studied. Special focus is laid on singular operator pencils and three different concepts of singularity of operator pencils are introduced. The…
The differential calculus on `non-standard' $h$-Minkowski spaces is given. In particular it is shown that, for them, it is possible to introduce coordinates and derivatives which are simultaneously hermitian.
In this work we use the tensorial language developed in [8] and [9] to differentiate functions of eigenvalues of symmetric matrices. We describe the formulae for the k-th derivative of such functions in two cases. The first case concerns…
We study the Hermitian supermatrix model involving an external source. We derive the determinantal formula for the supermatrix partition function, and also for the expectation value of the characteristic polynomial ratio, which yields the…
This paper is concerned with generalizations of the notion of principal eigenvalue in the context of space-time periodic cooperative systems. When the spatial domain is the whole space, the Krein-Rutman theorem cannot be applied and this…
In the last few years, the supersymmetry method was generalized to real-symmetric, Hermitean, and Hermitean self-dual random matrices drawn from ensembles invariant under the orthogonal, unitary, and unitary symplectic group, respectively.…
Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential…
In the article integer divisibility properties and related prime factors natural number representation concepts have been defined over the whole infinite hyperoperation hierarchy. The definitions have been made across and above of unique…
We rederive in a simplified version the Lehmann-Sommers eigenvalue distribution for the Gaussian ensemble of asymmetric real matrices, invariant under real orthogonal transformations, as a basis for a detailed derivation of a Pfaffian…
We describe symmetric diffusion operators where the spectral decomposition is given through a family of orthogonal polynomials. In dimension one, this reduces to the case of Hermite, Laguerre and Jacobi polynomials. In higher dimension,…
A remarkable property of Hermitian ensembles is their universal behavior, that is, once properly rescaled the eigenvalue statistics does not depend on particularities of the ensemble. Recently, normal matrix ensembles have attracted…
In this paper, we investigate the spectrum of the self adjoint differential operator with operator coefficitent in a separable Hilbert space. We also derive asymptotic formulas for the sum of eigenvalues of this operator.
We derive the connected correlation functions for eigenvalues of large Hermitian random matrices with independently distributed elements using both a diagrammatic and a renormalization group (RG) inspired approach. With the diagrammatic…
In the present work, eigenvalue distributions defined by a random rectangular matrix whose components are neither independently nor identically distributed are analyzed using replica analysis and belief propagation. In particular, we…
It is known that hermitean random matrix ensembles can be identified with symmetric coset spaces of Lie groups, or else with tangent spaces of the same. This results in a classification of random matrix ensembles as well as applications in…
We consider the limiting location and limiting distribution of the largest eigenvalue in real symmetric ($\beta$ = 1), Hermitian ($\beta$ = 2), and Hermitian self-dual ($\beta$ = 4) random matrix models with rank 1 external source. They are…
We study the joint probability density of the eigenvalues of a product of rectangular real, complex or quaternion random matrices in a unified way. The random matrices are distributed according to arbitrary probability densities, whose only…