Related papers: Universality of local eigenvalue statistics in ran…
We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay…
We develop a unified approach to universality of local scaling limits for eigenvalues of random normal matrices, or equivalently for planar Coulomb gases at inverse temperature $\beta=2$. The approach is direct in that it does not rely on…
We derive exact analytical expressions for correlation functions of singular values of the product of $M$ Ginibre matrices of size $N$ in the double scaling limit $M,N\rightarrow \infty$. The singular value statistics is described by a…
We prove the Wigner-Dyson-Mehta conjecture at fixed energy in the bulk of the spectrum for generalized symmetric and Hermitian Wigner matrices. Previous results concerning the universality of random matrices either require an averaging in…
We consider the block band matrices, i.e. the Hermitian matrices $H_N$, $N=|\Lambda|W$ with elements $H_{jk,\alpha\beta}$, where $j,k \in\Lambda=[1,m]^d\cap \mathbb{Z}^d$ (they parameterize the lattice sites) and $\alpha, \beta= 1,\ldots,…
We obtain the explicit rate of convergence $N^{-1/2 + \epsilon}$ for the gaps of generalized Wigner matrices in the bulk of the spectrum, for distributions of matrix entries possibly atomic and supported on enough points. The proof proceeds…
Eigenvalue correlations of random matrix ensembles as a function of an external perturbation are investigated vis the Dyson Brownian Motion Model in the situation where the level density has a hard edge singularity. By solving a linearized…
We study universal traits which emerge both in real-world complex datasets, as well as in artificially generated ones. Our approach is to analogize data to a physical system and employ tools from statistical physics and Random Matrix Theory…
We consider $n$ particles $0\leq x_1<x_2< \cdots < x_n < +\infty$, distributed according to a probability measure of the form $$ \frac{1}{Z_n}\prod_{1\leq i <j \leq n}(x_j-x_i)\prod_{1\leq i <j \leq…
We consider real, Gauss-divisible matrices $A_{t}=A+\sqrt{t}B$, where $B$ is from the real Ginibre ensemble. We prove that the bulk correlation functions converge to a universal limit for $t=O(N^{-1/3+\epsilon})$ if $A$ satisfies certain…
In this paper, we analyze the large n-limit for random matrix with external source with three distinct eigenvalues. And we confine ourselves in the Hermite case and the three distinct eigenvalues are $-a,0,a$. For the case $a^2>3$, we…
Universality of eigenvalue spacings is one of the basic characteristics of random matrices. We give the precise meaning of universality and discuss the standard universality classes (sine, Airy, Bessel) and their appearance in unitary,…
It is shown how the universal correlation function of Brezin and Zee, and Beenakker, for random matrix ensembles of Wigner-Dyson type with density support on a finite interval can be derived using a linear response argument and macroscopic…
We consider the product of n complex non-Hermitian, independent random matrices, each of size NxN with independent identically distributed Gaussian entries (Ginibre matrices). The joint probability distribution of the complex eigenvalues of…
This work is concerned with finite range bounds on the variance of individual eigenvalues of random covariance matrices, both in the bulk and at the edge of the spectrum. In a preceding paper, the author established analogous results for…
We show that eigenvalue correlations in unitary-invariant ensembles of large random matrices adhere to novel universal laws that only depend on a multicriticality of the bulk density of states near the soft edge of the spectrum. Our…
In this paper, we investigate the asymptotic spectrum of complex or real Deformed Wigner matrices $(M_N)_N$ defined by $M_N=W_N/\sqrt{N}+A_N$ where $W_N$ is an $N\times N$ Hermitian (resp., symmetric) Wigner matrix whose entries have a…
We consider the non-Hermitian analogue of the celebrated Wigner-Dyson-Mehta bulk universality phenomenon, i.e. that in the bulk the local eigenvalue statistics of a large random matrix with independent, identically distributed centred…
We develop a new method for deriving local laws for a large class of random matrices. It is applicable to many matrix models built from sums and products of deterministic or independent random matrices. In particular, it may be used to…
We consider $N\times N$ random matrices of the form $H = W + V$ where $W$ is a real symmetric Wigner matrix and $V$ a random or deterministic, real, diagonal matrix whose entries are independent of $W$. We assume subexponential decay for…