相关论文: General moments of matrix elements from circular o…
We investigate eigenvalue moments of matrices from Circular Orthogonal Ensemble multiplicatively perturbed by a permutation matrix. More precisely we investigate variance of the sum of the eigenvalues raised to power $k$, for arbitrary but…
Let $W$ be a random positive definite symmetric matrix distributed according to a real Wishart distribution and let $W^{-1}=(W^{ij})_{i,j}$ be its inverse matrix. We compute general moments $\mathbb{E} [W^{k_1 k_2} W^{k_3 k_4} ...…
This is a short introduction to Weingarten Calculus. Weingarten Calculus is a method to compute the joint moments of matrix variables distributed according to the Haar measure of compact groups.
Weingarten calculus is a completely general and explicit method to compute the moments of the Haar measure on compact subgroups of matrix algebras. Particular cases of this calculus were initiated by theoretical physicists -- including…
Given a uniform ensemble of quantum density matrices $\rho$, it is useful to calculate the mean value over this ensemble of a product of entries of $\rho$. We show how to calculate such moments in this paper. The answer involves well known…
We uncover a hidden Gaussian ensemble inside each of the three circular ensembles of random matrices, which provide novel diagrammatic rules for the calculation of moments. The matrices involved are generic complex for $\beta=2$, complex…
A method for computing integrals of polynomial functions on compact symmetric spaces is given. Those integrals are expressed as sums of functions on symmetric groups.
We establish a new connection between moments of $n \times n$ random matrices $X_n$ and hypergeometric orthogonal polynomials. Specifically, we consider moments $\mathbb{E}\mathrm{Tr} X_n^{-s}$ as a function of the complex variable $s \in…
In this tutorial paper, we formulate a two-dimensional integral-equation based method of moments approach for numerically computing the electromagnetic fields scattered from an azimuthally-rough dielectric cylinder or an axially-rough…
We develop a powerful framework to calculate expectation values of polynomials and moments on compact Lie groups based on elementary representation-theoretic arguments and an integration by parts formula. In the setting of lattice gauge…
A fundamental property of compact groups and compact quantum groups is the existence and uniqueness of a left and right invariant probability -- the Haar measure. This is a natural playground for classical and quantum probability, provided…
We introduce and study the Weingarten calculus for centered random permutation matrices in the symmetric group S_N. After presenting a formulation of the Weingarten calculus on the symmetric group, we derive a formula in the centered case,…
We investigate certain matrices composed of mixed, second-order moments of unitaries. The unitaries are taken from C*-algebras with moments taken with respect to traces, or, alternatively, from matrix algebras with the usual trace. These…
Using asymptotics of Toeplitz+Hankel determinants, we establish formulae for the asymptotics of the moments of the moments of the characteristic polynomials of random orthogonal and symplectic matrices, as the matrix-size tends to infinity.…
The problem of calculating the scaled limit of the joint moments of the characteristic polynomial, and the derivative of the characteristic polynomial, for matrices from the unitary group with Haar measure first arose in studies relating to…
We obtain for the Kempner series (i.e. harmonic series where certain digits are excluded from all denominators, for example the digit 9 in base 10) new representations as geometrically convergent series. The coefficients for these…
Special orthogonal matrices with rational elements form the group SO(n,Q), where Q is the field of rational numbers. A theorem describing the structure of an arbitrary matrix from this group is proved. This theorem yields an algorithm for…
The randomized quantum marginal problem asks about the joint distribution of the partial traces ("marginals") of a uniform random Hermitian operator with fixed spectrum acting on a space of tensors. We introduce a new approach to this…
We study the moment space corresponding to matrix measures on the unit circle. Moment points are characterized by non-negative definiteness of block Toeplitz matrices. This characterization is used to derive an explicit representation of…
A conversion matrix approach to solving network problems involving time-varying circuit components is applied to the method of moments for electromagnetic scattering analysis. Detailed formulations of this technique's application to the…