Related papers: Mixed Correlation Functions of the Two-Matrix Mode…

We consider four nontrivial ensembles involving Gaussian Wigner and Wishart matrices. These are relevant to problems ranging from multiantenna communication to random supergravity. We derive the matrix probability density, as well as the…

We introduce the concept of reflexive moment functional in two variables and the definition of reflexive orthogonal polynomial system. Also reverse matrices and their interesting algebraic properties are studied. Reverse matrices and…

The relation between the spectral decomposition of a self-adjoint operator which is realizable as a higher order recurrence operator and matrix-valued orthogonal polynomials is investigated. A general construction of such operators from…

The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…

Recursion formulae are derived for the calculation of two centre matrix elements of a radial function in relativistic quantum mechanics. The recursions are obtained between not necessarily diagonal radial eigensates using arbitrary radial…

Using random matrix technique we determine an exact relation between the eigenvalue spectrum of the covariance matrix and of its estimator. This relation can be used in practice to compute eigenvalue invariants of the covariance…

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 continue the study of the correlation functions for the point stochastic processes introduced in Part I (G.Olshanski, math.RT/9804086). We find an integral representation of all the correlation functions and their explicit expression in…

We study graph parameters whose associated edge-connection matrices have exponentially bounded rank growth. Our main result is an explicit construction of a large class of graph parameters with this property that we call mixed partition…

Strongly non-Gaussian ensembles of large random matrices possessing unitary symmetry and logarithmic level repulsion are studied both in presence and absence of hard edge in their energy spectra. Employing a theory of polynomials orthogonal…

We investigate the behaviour of the two-point correlation function in the context of passive scalars for non homogeneous, non isotropic forcing ensembles. Exact analytical computations can be carried out in the framework of the Kraichnan…

We consider here a particular quadratic equation linking two elements of a C-Algebra. By analysing powers of the unknowns, it appears a double sequence of polynomials related to classical Bernoulli polynomials. We get the generating…

We consider the biorthogonal polynomials associated to the two-matrix model where the eigenvalue distribution has potentials V_1,V_2 with arbitrary rational derivative and whose supports are constrained on an arbitrary union of intervals…

The ensemble inter-relations to be considered are special features of classical cases, where the joint eigenvalue probability density can be computed explicitly. Attention will be focussed too on the consequences of these inter-relations,…

We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional…

For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.

Exploiting the explicit bijection between the density of singular values and the density of eigenvalues for bi-unitarily invariant complex random matrix ensembles of finite matrix size, we aim at finding the induced probability measure on…

We propose a recursive algorithm for the calculation of multi-baryon correlation functions that combines the advantages of a recursive approach with those of the recently proposed unified contraction algorithm. The independent components of…

We discuss the product of independent induced quaternion ($\beta=4$) Ginibre matrices, and the eigenvalue correlations of this product matrix. The joint probability density function for the eigenvalues of the product matrix is shown to be…

Closed-form generating functions for counting one-face rooted hypermaps with a known number of darts by number of vertices and edges is found, using matrix integral expressions relating to the reduced density operator of a bipartite quantum…