Related papers: The Ginibre ensemble of real random matrices and i…
We study the normal matrix model, also known as the two-dimensional one-component plasma at a specific temperature, with merging singularity. As the number $n$ of particles tends to infinity we obtain the limiting local correlation kernel…
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…
The Ginibre ensemble of complex random matrices is studied. The complex valued random variable of second difference of complex energy levels is defined. For the N=3 dimensional ensemble are calculated distributions of second difference, of…
We study the statistics of the number of real eigenvalues in the elliptic deformation of the real Ginibre ensemble. As the matrix dimension grows, the law of large numbers and the central limit theorem for the number of real eigenvalues are…
We study unitary invariant random matrix ensembles with singular potentials. We obtain asymptotics for the partition functions associated to the Laguerre and Gaussian Unitary Ensembles perturbed with a pole of order $k$ at the origin, in…
We study the deformed complex Ginibre ensemble $H=A_0+H_0$, where $H_0$ is the complex matrix with iid Gaussian entries, and $A_0$ is some general $n\times n$ matrix (it can be random and in this case it is independent of $H_0$). Assuming…
The paper is concerned with the asymptotic behavior of the correlation functions of the characteristic polynomials of non-Hermitian random matrices with independent entries. It is shown that the correlation functions behave like that for…
We calculate eigenvector statistics in an ensemble of non-Hermitian matrices describing open quantum systems [F. Haake et al., Z. Phys. B 88, 359 (1992)] in the limit of large matrix size. We show that ensemble-averaged eigenvector…
We consider non-gaussian ensembles of random normal matrices with the constraint that the ensembles are invariant under unitary transformations. We show that the level density of eigenvalues exhibits disk to ring transition in the complex…
Non-Hermitian random matrices enjoy non-trivial correlations in the statistics of their eigenvectors. We study the overlap among left and right eigenvectors in Ginibre ensembles with quaternion valued Gaussian matrix elements. This concept…
We present a five-step method for the calculation of eigenvalue correlation functions for various ensembles of real random matrices, based upon the method of (skew-) orthogonal polynomials. This scheme systematises existing methods and also…
We consider non-Gaussian extensions of the elliptic Ginibre ensemble of complex non-Hermitian random matrices by fixing the trace $\operatorname{Tr}(XX^*)$ of the matrix $X$ with a hard or soft constraint. These ensembles have correlated…
It is known that the bulk scaling limit of the real eigenvalues for the real Ginibre ensemble is equal in distribution to the rescaled $t \to \infty$ limit of the annihilation process $A + A \to \emptyset$. Furthermore, deleting each…
We study random normal matrix models whose eigenvalues tend to be distributed within a narrow "band" around the unit circle of width proportional to $\frac1n$, where $n$ is the size of matrices. For general radially symmetric potentials…
Universal limits for the eigenvalue correlation functions in the bulk of the spectrum are shown for a class of nondeterminantal random matrices known as the fixed trace ensemble.
We show that the correlation functions associated to symmetrized increasing subsequence problems can be expressed as pfaffians of certain antisymmetric matrix kernels, thus generalizing the result of math.RT/9907127 for the unsymmetrized…
We study the Gaussian hermitian random matrix ensemble with an external matrix which has an arbitrary number of eigenvalues with arbitrary multiplicity. We compute the limiting eigenvalues correlations when the size of the matrix goes to…
We show that as $n$ changes, the characteristic polynomial of the $n\times n$ random matrix with i.i.d. complex Gaussian entries can be described recursively through a process analogous to P\'olya's urn scheme. As a result, we get a random…
We compute averages of products and ratios of characteristic polynomials associated with Orthogonal, Unitary, and Symplectic Ensembles of Random Matrix Theory. The pfaffian/determinantal formulas for these averages are obtained, and the…
We consider ensembles of real symmetric band matrices with entries drawn from an infinite sequence of exchangeable random variables, as far as the symmetry of the matrices permits. In general the entries of the upper triangular parts of…