Related papers: Determinants of Random Block Hankel Matrices
We investigate the asymptotics of the determinant of N by N Hankel matrices generated by Fisher-Hartwig symbols defined on the real line, as N becomes large. Such objects are natural analogues of Toeplitz determinants generated by…
This paper studies the behaviour of the empirical eigenvalue distribution of large random matrices W_N W_N* where W_N is a ML x N matrix, whose M block lines of dimensions L x N are mutually independent Hankel matrices constructed from…
Starting from Montgomery's conjecture, there has been a substantial interest on the connections of random matrix theory and the theory of L-functions. In particular, moments of characteristic polynomials of random matrices have been…
In this paper we investigate the smallest eigenvalue, denoted as $\la_N,$ of a $(N+1)\times (N+1)$ Hankel or moments matrix, associated with the weight, $w(x)=\exp(-x^{\bt}),x>0,\bt>0$, in the large $N$ limit. Using a previous result, the…
We consider the Jacobi operator (T,D(T)) associated with an indeterminate Hamburger moment problem, and present countable subsets S of the domain D(T) such that span(S) is dense in \ell^2. As an example we have…
For random matrix ensembles with unitary symmetry, there is interest in the large $N$ form of the moments of the absolute value of the characteristic polynomial for their relevance to the Riemann zeta function on the critical line, and to…
Number theorists have studied extensively the connections between the distribution of zeros of the Riemann $\zeta$-function, and of some generalizations, with the statistics of the eigenvalues of large random matrices. It is interesting to…
We examine the asymptotics of the moments of characteristic polynomials of $N\times N$ matrices drawn from the Hermitian ensembles of Random Matrix Theory, in the limit as $N\to\infty$. We focus in particular on the Gaussian Unitary…
We establish asymptotic formulas for the determinants of finite Toeplitz + Hankel matrices of size N, as N goes to infinity for singular generating functions defined on the unit circle in the special case where the generating function is…
Denoting by $P_N(A,\theta)=\det(I-Ae^{-i\theta})$ the characteristic polynomial on the unit circle in the complex plane of an $N\times N$ random unitary matrix $A$, we calculate the $k$th moment, defined with respect to an average over…
Duality identities in random matrix theory for products and powers of characteristic polynomials, and for moments, are reviewed. The structure of a typical duality identity for the average of a positive integer power $k$ of the…
We study Helson matrices (also known as multiplicative Hankel matrices), i.e. infinite matrices of the form $M(\alpha) = \{\alpha(nm)\}_{n,m=1}^\infty$, where $\alpha$ is a sequence of complex numbers. Helson matrices are considered as…
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…
In this paper we determine the asymptotics of the determinants of truncated Wiener-Hopf plus Hankel operators $\det(W_R(a)\pm H_R(a))$ as $R$ tends to infinity for symbols $a(x)=(x^2/(1+x^2))^\beta$ with the parameter $\beta$ being of small…
We obtain the explicit evaluations of the Hankel determinants of the formal power series $\prod_{k\geq 0}(1+Jx^{3^{k}})$ where $J={(\sqrt{-3}-1)}/2$, and prove that the sequence of Hankel determinants is an aperiodic automatic sequence…
The eigenvalue correlations of random matrices from the Jacobi Unitary Ensemble have a known asymptotic behavior as their size tends to infinity. In the bulk of the spectrum the behavior is described in terms of the sine kernel, and at the…
We study the moment-generating functions (MGF) for linear eigenvalue statistics of Jacobi unitary, symplectic and orthogonal ensembles. By expressing the MGF as Fredholm determinants of kernels of finite rank, we show that the mean and…
We consider the singular values of certain Young diagram shaped random matrices. For block-shaped random matrices, the empirical distribution of the squares of the singular eigenvalues converges almost surely to a distribution whose moments…
The purpose of this paper is to describe asymptotic formulas for determinants of a sum of finite Toeplitz and Hankel matrices with singular generating functions. The formulas are similar to those of the analogous problem for finite Toeplitz…
We study random partitions $\lambda=(\lambda_1,\lambda_2,...,\lambda_d)$ of $n$ whose length is not bigger than a fixed number $d$. Suppose a random partition $\lambda$ is distributed according to the Jack measure, which is a deformation of…