Related papers: Mixed Correlation Functions of the Two-Matrix Mode…
We calculate the autocorrelation function for the characteristic polynomial of a random matrix in the microscopic scaling regime. While results fitting this description have be proved before, we will cover all values of inverse temperature…
A general model-independent discussion of mesonic correlation functions is given. We derive new inequalities, including one stronger than Weingarten's inequality. Mesonic correlation functions are calculated in the random instanton vacuum…
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…
We present a simple and consistent way to compute correlation functions in interacting theories with non-trivial phase diagram. As an example we show how to consistently compute the four-point function in three dimensional…
We derive the connected correlation functions for eigenvalues of large Hermitian random matrices with independently distributed elements using both a diagrammatic and a renormalization group (RG) inspired approach. With the diagrammatic…
We develop the study of a particular class of biorthogonal measures, encompassing at the same time several random matrix models and partition functions of polymers. This general framework allows us to characterize the partition functions of…
Orthogonal polynomials and multiple orthogonal polynomials are interesting special functions because there is a beautiful theory for them, with many examples and useful applications in mathematical physics, numerical analysis, statistics…
The ability to measure characteristics of source shapes using non-identical particle correlations is discussed. Both strong-interaction induced and Coulomb induced correlations are shown to provide sensitivity to source shapes. By…
We compute the large scale (macroscopic) correlations in ensembles of normal random matrices with an arbitrary measure and in ensembles of general non-Hermition matrices with a class of non-Gaussian measures. In both cases the eigenvalues…
We establish a general relation between the diagonal correlator of eigenvectors and the spectral Green's function for non-hermitian random-matrix models in the large-N limit. We apply this result to a number of non-hermitian random-matrix…
The two-matrix model is defined on pairs of Hermitian matrices $(M_1,M_2)$ of size $n\times n$ by the probability measure $$\frac{1}{Z_n} \exp\left(\textrm{Tr} (-V(M_1)-W(M_2)+\tau M_1M_2)\right)\ dM_1\ dM_2, $$ where $V$ and $W$ are given…
We derive the double scaling limit of eigenvalue correlations in the random matrix model at critical points and we relate the limiting correlation functions to a nonlinear hierarchy of ordinary differential equations.
We give a new method for the evaluation of a class of integrals of rational symmetric functions in N pairs of variables {x_a, y_a}_{a=1,... N} arising in coupled matrix models, valid for a broad class of two-variable measures. The result is…
In this paper we consider the problem of approximating vector-valued functions over a domain $\Omega$. For this purpose, we use matrix-valued reproducing kernels, which can be related to Reproducing kernel Hilbert spaces of vectorial…
We know that the marginals in a multinomial distribution are binomial variates exhibiting a negative correlation. But we can construct two linear combinations of such marginals in such a way to obtain a positive correlation. We discuss the…
Often, polynomials or rational functions, orthogonal for a particular inner product are desired. In practical numerical algorithms these polynomials are not constructed, but instead the associated recurrence relations are computed.…
We investigate the generating functions of multi-colored discrete disks with non-homogenous boundary conditions in the context of the Hermitian multi-matrix model where the matrices are coupled in an open chain. We show that the study of…
Multiple orthogonal polynomials are a generalization of orthogonal polynomials in which the orthogonality is distributed among a number of orthogonality weights. They appear in random matrix theory in the form of special determinantal point…
The generating function that records the sizes of directed circuit partitions of a connected 2-in, 2-out digraph D can be determined from the interlacement graph of D with respect to a directed Euler circuit; the same is true of the…
Mixed orthogonal Laurent polynomials on the unit circle of CMV type are constructed utilizing a matrix of moments and its Gauss--Borel factorization and employing a multiple extension of the CMV ordering. A systematic analysis of the…