相关论文: Smoothed Correlators For Symmetric Double-Well Mat…

Exact eigenvalue correlation functions are computed for large $N$ hermitian one-matrix models with eigenvalues distributed in two symmetric cuts. An asymptotic form for orthogonal polynomials for arbitrary polynomial potentials that support…

We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in…

A recursive method is derived to calculate all eigenvalue correlation functions of a random hermitian matrix in the large size limit, and after smoothing of the short scale oscillations. The property that the two-point function is…

Computing the eigenvectors and eigenvalues of a perturbed matrix can be remarkably difficult when the unperturbed matrix has repeated eigenvalues. In this work we show how the limiting eigenvectors and eigenvalues of a symmetric matrix…

Data sets collected at different times and different observing points can possess correlations at different times $and$ at different positions. The doubly correlated Wishart model takes both into account. We calculate the eigenvalue density…

Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional data, particularly beyond the case of "null models" for which…

Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…

This paper summarizes some work I've been doing on eigenvalue correlators of Random Matrix Models which show some interesting behaviour. First we consider matrix models with gaps in there spectrum or density of eigenvalues. The…

We report on calculations of smoothed spectral correlations in the two-dimensional Anderson model for weak disorder. As pointed out in (M. Wilkinson, J. Phys. A: Math. Gen. 21, 1173 (1988)), an analysis of the smoothing dependence of the…

Spectral correlations in unitary invariant, non-Gaussian ensembles of large random matrices possessing an eigenvalue gap are studied within the framework of the orthogonal polynomial technique. Both local and global characteristics of…

We present a new algorithm for solving an eigenvalue problem for a real symmetric arrowhead matrix. The algorithm computes all eigenvalues and all components of the corresponding eigenvectors with high relative accuracy in $O(n^{2})$…

We show how to calculate correlation functions of two matrix models. Our method consists in making full use of the integrable hierarchies and their reductions, which were shown in previous papers to naturally appear in multi--matrix models.…

The eigenvalue probability density function for symplectic invariant random matrix ensembles can be generalised to discrete settings involving either a linear or exponential lattice. The corresponding correlation functions can be expressed…

We obtain general, exact formulas for the overlaps between the eigenvectors of large correlated random matrices, with additive or multiplicative noise. These results have potential applications in many different contexts, from quantum…

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 propose a second-order accurate method to estimate the eigenvectors of extremely large matrices thereby addressing a problem of relevance to statisticians working in the analysis of very large datasets. More specifically, we show that…

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…

We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…

In this note, we present an algorithm that yields many new methods for constructing doubly stochastic and symmetric doubly stochastic matrices for the inverse eigenvalue problem. In addition, we introduce new open problems in this area that…

Repeated measurements are common in many fields, where random variables are observed repeatedly across different subjects. Such data have an underlying hierarchical structure, and it is of interest to learn covariance/correlation at…