相关论文: Multiplying unitary random matrices - universality…
We develop a simple algorithm to generate random variables described by densities equaling squared Hermite functions. As an application, we show how to generate a randomly chosen eigenvalue of a matrix from the Gaussian Unitary Ensemble…
We study the joint probability density of the eigenvalues of a product of rectangular real, complex or quaternion random matrices in a unified way. The random matrices are distributed according to arbitrary probability densities, whose only…
This paper is concerned with complex eigenvalues of truncated unitary quaternion matrices equipped with the Haar measure. The joint eigenvalue probability density function is obtained for truncations of any size. We also obtain the spectral…
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
We consider large non-Hermitian real or complex random matrices $X$ with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of…
We consider two non-Gaussian ensembles of large Hermitian random matrices with strong level confinement and show that near the soft edge of the spectrum both scaled density of states and eigenvalue correlations follow so-called Airy laws…
Products of truncated unitary matrices, independently and uniformly drawn from the unitary group, can be used to study universal aspects of monitored quantum circuits. The von Neumann entropy of the corresponding density matrix decreases…
For general large non-Hermitian random matrices $X$ and deterministic normal deformations $A$, we prove that the local eigenvalue statistics of $A+X$ close to the critical edge points of its spectrum are universal. This concludes the proof…
Recently, the joint probability density functions of complex eigenvalues for products of independent complex Ginibre matrices have been explicitly derived as determinantal point processes. We express truncated series coming from the…
We investigate the spectral properties of the product of $M$ complex non-Hermitian random matrices that are obtained by removing $L$ rows and columns of larger unitary random matrices uniformly distributed on the group ${\rm U}(N+L)$. Such…
We show that randomly choosing the matrices in a completely positive map from the unitary group gives a quantum expander. We consider Hermitian and non-Hermitian cases, and we provide asymptotically tight bounds in the Hermitian case on the…
We describe a new universality class for unitary invariant random matrix ensembles. It arises in the double scaling limit of ensembles of random $n \times n$ Hermitian matrices $Z_{n,N}^{-1} |\det M|^{2\alpha} e^{-N \Tr V(M)} dM$ with…
In this review we summarise recent results for the complex eigenvalues and singular values of finite products of finite size random matrices, their correlation functions and asymptotic limits. The matrices in the product are taken from…
Consider two types of products of independent random matrices, including products of Ginibre matrices and inverse Ginibre matrices and products of truncated Haar unitary matrices and inverse truncated Haar matrices. Each product matrix has…
It has been observed that the statistical distribution of the eigenvalues of random matrices possesses universal properties, independent of the probability law of the stochastic matrix. In this article we find the correlation functions of…
In order to have a better understanding of finite random matrices with non-Gaussian entries, we study the $1/N$ expansion of local eigenvalue statistics in both the bulk and at the hard edge of the spectrum of random matrices. This gives…
We generally study the density of eigenvalues in unitary ensembles of random matrices from the recurrence coefficients with regularly varying conditions for the orthogonal polynomials. First we calculate directly the moments of the density.…
We investigate the universality of singular value and eigenvalue distributions of matrix valued functions of independent random matrices and apply these general results in several examples. In particular we determine the limit distribution…
We consider $N\times N$ Hermitian Wigner random matrices $H$ where the probability density for each matrix element is given by the density $\nu(x)= e^{- U(x)}$. We prove that the eigenvalue statistics in the bulk is given by Dyson sine…
We study the densities of limiting distributions of squared singular values of high-dimensional matrix products composed of independent complex Gaussian (complex Ginibre) and truncated unitary matrices which are taken from Haar distributed…