Related papers: Universality for random matrices and log-gases

We prove universality of local eigenvalue statistics in the bulk of the spectrum for orthogonal invariant matrix models with real analytic potentials with one interval limiting spectrum. Our starting point is the Tracy-Widom formula for the…

We analyze the distribution of eigenvectors for mesoscopic, mean-field perturbations of diagonal matrices in the bulk of the spectrum. Our results apply to a generalized $N\times N$ Rosenzweig-Porter model. We prove that the eigenvectors…

This paper is aimed at deriving the universality of the largest eigenvalue of a class of high-dimensional real or complex sample covariance matrices of the form $\mathcal{W}_N=\Sigma^{1/2}XX^*\Sigma ^{1/2}$. Here, $X=(x_{ij})_{M,N}$ is an…

The beautiful and profound result that the first eigenvalue of Schroedinger operator can be interpreted as a large deviation of certain kind of Brownian motion leads to possible existence of universality in the distribution of ground state…

It was shown roughly thirty years ago that the density correlations of eigenvalues of large random matrices display a universal form, independent of most of the details of the distribution of the random matrix itself. We show that when the…

We consider a toy model for the study of monitored dynamics in a many-body quantum systems. We study the stochastic Schrodinger equation resulting from the continuous monitoring with a rate $\Gamma$ of a random hermitian operator chosen at…

We consider 1d random Hermitian $N\times N$ block band matrices consisting of $W\times W$ random Gaussian blocks (parametrized by $j,k \in\Lambda=[1,n]\cap \mathbb{Z}$, $N=nW$) with a fixed entry's variance…

We prove that a very general class of $N\times N$ Hermitian random band matrices is in the delocalized phase when the band width $W$ exceeds the critical threshold, $W\gg \sqrt{N}$. In this regime, we show that, in the bulk spectrum, the…

We study the eigenvalues of the covariance matrix $\frac{1}{n}M^*M$ of a large rectangular matrix $M=M_{n,p}=(\zeta_{ij})_{1\leq i\leq p;1\leq j\leq n}$ whose entries are i.i.d. random variables of mean zero, variance one, and having finite…

The total energy of an eigenstate in a composite quantum system tends to be distributed equally among its constituents. We identify the quantum fluctuation around this equipartition principle in the simplest disordered quantum system…

Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such…

We consider a single particle spectrum as given by the eigenvalues of the Wigner-Dyson ensembles of random matrices, and fill consecutive single particle levels with n fermions. Assuming that the fermions are non-interacting, we show that…

We study generalizations of the Gross--Witten--Wadia unitary matrix model for the special orthogonal and symplectic groups. We show using a standard Coulomb gas treatment -- employing a path integral formalism for the ungapped phase and…

We consider an $N$ by $N$ real or complex generalized Wigner matrix $H_N$, whose entries are independent centered random variables with uniformly bounded moments. We assume that the variance profile, $s_{ij}:=\mathbb{E} |H_{ij}|^2$,…

We study the ultrametric random matrix ensemble, whose independent entries have variances decaying exponentially in the metric induced by the tree topology on $\mathbb{N}$, and map out the entire localization regime in terms of…

Using Beck and Cohen's superstatistics, we introduce in a systematic way a family of generalised Wishart-Laguerre ensembles of random matrices with Dyson index $\beta$ = 1,2, and 4. The entries of the data matrix are Gaussian random…

We give a proof of the Universality Conjecture for orthogonal and symplectic ensembles of random matrices in the scaling limit for a class of weights w(x)=exp(-V(x)) where V is a polynomial, V(x)=kappa_{2m}x^{2m}+..., kappa_{2m}>0. For such…

In this paper we generalize the concept of Wigner function in the case of quantum mechanics with a minimum length scale arising due to the application of a generalized uncertainty principle (GUP). We present the phase space formulation of…

The Hungarian physicist Eugene Wigner introduced random matrix models in physics to describe the energy spectra of atomic nuclei. As such, the main goal of Random Matrix Theory (RMT) has been to derive the eigenvalue statistics of matrices…

We discuss the concept of width-to-spacing ratio which plays the central role in the description of local spectral statistics of evolution operators in multiplicative and additive stochastic processes for random matrices. We show that the…