Related papers: Counting formulas associated with some random matr…
We develop a combinatorial model of the associated Hermite polynomials and their moments, and prove their orthogonality with a sign-reversing involution. We find combinatorial interpretations of the moments as complete matchings, connected…
We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.
Moments of the characteristic polynomial of a random matrix taken from any of the three ensembles, orthogonal, unitary or symplectic, are given either as a determinant or a pfaffian or as a sum of determinants. For gaussian ensembles…
This paper defines and develops cycle indices for the finite classical groups. These tools are then applied to study properties of a random matrix chosen uniformly from one of these groups. Properties studied by this technique will include…
We consider $N\times N$ random matrices of the form $H=W+V$ where $W$ is a real symmetric or complex Hermitian Wigner matrix and $V$ is a random or deterministic, real, diagonal matrix whose entries are independent of $W$. We assume…
It is a classical result of Wigner that for an hermitian matrix with independent entries on and above the diagonal, the mean empirical eigenvalue distribution converges weakly to the semicircle law as matrix size tends to infinity. In this…
In this paper, a time series model with coefficients that take values from random matrix ensembles is proposed. Formal definitions, theoretical solutions, and statistical properties are derived. Estimation and forecast methodologies for…
The purpose of the present paper is to establish moment estimates of Rosenthal type for a rather general class of random variables satisfying certain bounds on the cumulants. We consider sequences of random variables which satisfy a central…
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…
Gaussian and Chiral Beta-Ensembles, which generalise well known orthogonal (Beta=1), unitary (Beta=2), and symplectic (Beta=4) ensembles of random Hermitian matrices, are considered. Averages are shown to satisfy duality relations like…
We introduce a notion of computable randomness for infinite sequences that generalises the classical version in two important ways. First, our definition of computable randomness is associated with imprecise probability models, in the sense…
We study some connections between the random moment problem and the random matrix theory. A uniform draw in a space of moments can be lifted into the spectral probability measure of the pair (A,e) where A is a random matrix from a classical…
We give a constructive proof for the superbosonization formula for invariant random matrix ensembles, which is the supersymmetry analog of the theory of Wishart matrices. Formulas are given for unitary, orthogonal and symplectic symmetry,…
We show that quaternionic Gaussian random variables satisfy a generalization of the Wick formula for computing the expected value of products in terms of a family of graphical enumeration problems. When applied to the quaternionic Wigner…
This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the…
The Gaussian unitary random matrix ensembles satisfying some additional symmetry conditions are considered. The effect of these conditions on the limiting normalized counting measures and correlation functions is studied.
We numerically analyze the random matrix ensembles of real-symmetric matrices with column/row constraints for many system conditions e.g. disorder type, matrix-size and basis-connectivity. The results reveal a rich behavior hidden beneath…
Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely…
The topic of this paper is the typical behavior of the spectral measures of large random matrices drawn from several ensembles of interest, including in particular matrices drawn from Haar measure on the classical Lie groups, random…
We present a simple, yet useful result about the expected value of the determinant of random sum of rank-one matrices. Computing such expectations in general may involve a sum over exponentially many terms. Nevertheless, we show that an…