Related papers: Eigenvalue correlations on Hyperelliptic Riemann s…

We consider large non-Hermitian random matrices $X$ with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are asymptotically Gaussian for test functions having…

We deepen the study of Dirichlet eigenvalues in bounded domains where a thin tube is attached to the boundary. As its section shrinks to a point, the problem is spectrally stable and we quantitatively investigate the rate of convergence of…

Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction…

We show that the average characteristic polynomial P_n(z) = E [\det(zI-M)] of the random Hermitian matrix ensemble Z_n^{-1} \exp(-Tr(V(M)-AM))dM is characterized by multiple orthogonality conditions that depend on the eigenvalues of the…

In a recent work Killip and Nenciu gave random recurrences for the characteristic polynomials of certain unitary and real orthogonal upper Hessenberg matrices. The corresponding eigenvalue p.d.f.'s are beta-generalizations of the classical…

The result of performing integrations over connection type variables in the path integral for the discrete field theory may be poorly defined in the case of non-compact gauge group with the Haar measure exponentially growing in some…

Models of disorder with a direction (constant imaginary vector-potential) are considered. These non-Hermitian models can appear as a result of computation for models of statistical physics using transfer matrix technique or describe…

We consider random matrix ensembles on the set of Hermitian matrices that are heavy tailed, in particular not all moments exist, and that are invariant under the conjugate action of the unitary group. The latter property entails that the…

For bounded domains, eigenvalues and eigenfunctions of double layer potentials are considered. The aim of this paper is to establish some relationships between eigenvalues, eigenfunctions and the geometry of domain boundaries.

We consider asymptotic behavior of the correlation functions of the characteristic polynomials of the hermitian sample covariance matrices $H_n=n^{-1}A_{m,n}^*A_{m,n}$, where $A_{m,n}$ is a $m\times n$ complex matrix with independent and…

If $A$ is an $n \times n$ Hermitian matrix with eigenvalues $\lambda_1(A),\dots,\lambda_n(A)$ and $i,j = 1,\dots,n$, then the $j^{\mathrm{th}}$ component $v_{i,j}$ of a unit eigenvector $v_i$ associated to the eigenvalue $\lambda_i(A)$ is…

A discrete eigenvalue E_n of a Schroedinger operator H = -\Delta + vf(r) is given, as a function F_n(v) of the coupling parameter v\ge v_c. It is shown how the potential shape f(x) can be reconstructed from F_n(v). A constructive inversion…

The confluent hypergeometric point process represents a universality class which arises in a variety of different but related areas. It particularly describes the local statistics of eigenvalues in the bulk of spectrum near a Fisher-Hartwig…

We introduce an approximation to the short-range correlation energy functional with multide-terminantal reference involved in a variant of range-separated density-functional theory. This approximation is a local functional of the density,…

We derive asymptotic expansions of the current, the electrostatic capacity, and the far-field of the electrostatic potential resulting from small perturbations in the shape of an isolated conductor with $\mathcal{C}^2$-surface. Our…

We study matrix integrals of the form $$\int_{\mathrm{USp(2n)}}\prod_{j=1}^k\mathrm{tr}(U^j)^{a_j}\mathrm d U,$$ where $a_1,\ldots,a_r$ are natural numbers and integration is with respect to the Haar probability measure. We obtain a compact…

We establish precise right-tail small deviation estimates for the largest eigenvalue of real symmetric and complex Hermitian matrices whose entries are independent random variables with uniformly bounded moments. The proof relies on a Green…

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…

It has been observed that the statistical distribution of the eigenvalues of random matrices possesses universal properties, independent of the probability law of the stochastic matrix. In this article we find the correlation functions of…

We prove the Central Limit Theorem for the number of eigenvalues near the spectrum edge for hermitian ensembles of random matrices. To derive our results, we use a general theorem, essentially due to Costin and Lebowitz, concerning the…