Related papers: Universality in Gaussian Random Normal Matrices

We establish universality of local eigenvalue correlations in unitary random matrix ensembles (1/Z_n) |\det M|^{2\alpha} e^{-n\tr V(M)} dM near the origin of the spectrum. If V is even, and if the recurrence coefficients of the orthogonal…

The universal connected correlations proposed recently between eigenvalues of unitary random matrices is examined numerically. We perform an ensemble average by the Monte Carlo sampling. Although density of eigenvalues and a bare…

The microscopic correlation functions of non-chiral random matrix models with complex eigenvalues are analyzed for a wide class of non-Gaussian measures. In the large-N limit of weak non-Hermiticity, where N is the size of the complex…

This paper establishes the universality of parametric correlations of eigenfunctions in chaotic and weakly disordered systems. We demonstrate this universality in the framework of the gaussian random matrix process and obtain predictions…

We consider a Gaussian random matrix with correlated entries that have a power law decay of order $d>2$ and prove universality for the extreme eigenvalues. A local law is proved using the self-consistent equation combined with a…

The behavior of correlation functions is studied in a class of matrix models characterized by a measure $\exp(-S)$ containing a potential term and an external source term: $S=N\tr(V(M)-MA)$. In the large $N$ limit, the short-distance…

We show that the linear statistics of eigenvalues of circulant matrix obey the Gaussian central limit theorem for a large class of input sequences.

A remarkable property of Hermitian ensembles is their universal behavior, that is, once properly rescaled the eigenvalue statistics does not depend on particularities of the ensemble. Recently, normal matrix ensembles have attracted…

This thesis reviews recent progress on products of random matrices from the perspective of exactly solved Gaussian random matrix models. We derive exact formulae for the correlation functions for the eigen- and singular values at arbitrary…

We consider a product of an arbitrary number of independent rectangular Gaussian random matrices. We derive the mean densities of its eigenvalues and singular values in the thermodynamic limit, eventually verified numerically. These…

Let $\widetilde{X}_{M\times N}$ be a rectangular data matrix with independent real-valued entries $[\widetilde{x}_{ij}]$ satisfying $\mathbb {E}\widetilde{x}_{ij}=0$ and $\mathbb {E}\widetilde{x}^2_{ij}=\frac{1}{M}$, $N,M\to\infty$. These…

It is a result of Ginibre that the normalized bulk $k$-point correlation functions of a complex $n\times n$ Gaussian matrix with independent entries of mean zero and unit variance are asymptotically given by the determinantal point process…

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 extend a recent theory of parametric correlations in the spectrum of random matrices to study the response to an external perturbation of eigenvalues near the soft edge of the support. We demonstrate by explicit non-perturbative…

We prove a universality theorem for learning with random features. Our result shows that, in terms of training and generalization errors, a random feature model with a nonlinear activation function is asymptotically equivalent to a…

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…

We describe an approach to universality limits for orthogonal polynomials on the real line which is completely local and uses only the boundary behavior of the Weyl m-function at the point. We show that bulk universality of the…

We demonstrate the convergence of the characteristic polynomial of several random matrix ensembles to a limiting universal function, at the microscopic scale. The random matrix ensembles we treat are classical compact groups and the…

The universality phenomenon asserts that the distribution of the eigenvalues of random matrix with i.i.d. zero mean, unit variance entries does not depend on the underlying structure of the random entries. For example, a plot of the…

We prove universality at the edge for rescaled correlation functions of Wigner random matrices in the limit $n\to +\infty$. As a corollary, we show that, after proper rescaling, the 1st, 2nd, 3rd, etc. eigenvalues of Wigner random hermitian…