Related papers: Duality in random matrix ensembles for all Beta
We study orthogonal and symplectic matrix models with polynomial potentials and multi interval supports of the equilibrium measure. For these models we find the bounds (similar to the case of hermitian matrix models) for the rate of…
We study multilevel matrix ensembles at general beta by identifying them with a class of processes defined via the branching rules for multivariate Bessel and Heckman-Opdam hypergeometric functions. For beta = 1, 2, we express the joint…
We derive the joint probability distribution of the first two spectral moments for the G$\beta$E random matrix ensembles in N dimensions for any N. This is achieved by making use of two complementary invariants of the domain in…
Recent theoretical studies of chaotic scattering have encounted ensembles of random matrices in which the eigenvalue probability density function contains a one-body factor with an exponent proportional to the number of eigenvalues. Two…
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
We investigate the eigenvalues statistics of ensembles of normal random matrices when their order N tends to infinite. In the model the eigenvalues have uniform density within a region determined by a simple analytic polynomial curve. We…
Using an elementary approach involving the Euler Beta function and the binomial theorem, we derive two polynomial identities; one of which is a generalization of a known polynomial identity. Two well-known combinatorial identities, namely…
Correlation functions involving products and ratios of half-integer powers of characteristic polynomials of random matrices from the Gaussian Orthogonal Ensemble (GOE) frequently arise in applications of Random Matrix Theory (RMT) to…
The paper continues previous works which study the behavior of second correlation function of characteristic polynomials of the special case of $n\times n$ one-dimensional Gaussian Hermitian random band matrices, when the covariance of the…
An explicit formula for the mean spectral measure of a random Jacobi matrix is derived. The matrix may be regarded as the limit of Gaussian beta ensemble (G$\beta$E) matrices as the matrix size $N$ tends to infinity with the constraint that…
The groups $O(N)$ and $Sp(N)$ are related by an analytic continuation to negative values of $N$, $O(-N)\simeq Sp(N)$. This duality has been studied for vector models, $SO(N)$ and $Sp(N)$ gauge theories, as well as some random matrix…
Non-Hermitian random matrices with statistical spectral characteristics beyond the standard Ginibre ensembles have recently emerged in the description of dissipative quantum many-body systems as well as in non-ergodic wave transport in…
We compute exact asymptotic of the statistical density of random matrices belonging to the Generalized Gaussian orthogonal, unitary and symplectic ensembles such that there no eigenvalues in the interval $[\sigma, +\infty[$. In particular,…
We solve the complex extension of the chiral Gaussian Symplectic Ensemble, defined as a Gaussian two-matrix model of chiral non-Hermitian quaternion real matrices. This leads to the appearance of Laguerre polynomials in the complex plane…
According to the classification scheme of the generalized random matrix ensembles, we present various kinds of concrete examples of the generalized ensemble, and derive their joint density functions in an unified way by one simple formula…
We investigate spectral conditions on Hermitian matrices of roots of unity. Our main results are conjecturally sharp upper bounds on the number of residue classes of the characteristic polynomial of such matrices modulo ideals generated by…
Moments of secular and inverse secular coefficients, averaged over random matrices from classical groups, are related to the enumeration of non-negative matrices with prescribed row and column sums. Similar random matrix averages are…
We consider the following problem: When do alternate eigenvalues taken from a matrix ensemble themselves form a matrix ensemble? More precisely, we classify all weight functions for which alternate eigenvalues from the corresponding…
The paper addresses the calculation of correlation functions of permanental polynomials of matrices with random entries. By exploiting a convenient contour integral representation of the matrix permanent some explicit results are provided…
A "mysterious" relation between the number variance and the variance of the $L$-th ordered eigenvalue, first suggested by French et al. [Ann. Phys. 113, 277 (1978)], is revisited and proven to be asymptotically exact for the $\beta=2$ Dyson…