Related papers: Eigenvalue Statistics for CMV Matrices: From Poiss…
We analyze the eigenvalue statistics of the staggered Dirac operator above $T_{c}$ in QCD with 2+1 flavors of dynamical quarks. We use physical quark masses in our simulations. We compare the eigenvalue statistics from several parts of the…
The spectra of empirical correlation matrices, constructed from multivariate data, are widely used in many areas of sciences, engineering and social sciences as a tool to understand the information contained in typically large datasets. In…
We numerically analyze the statistical properties of complex system with conditions subjecting the matrix elements to a set of specific constraints besides symmetry, resulting in various structures in their matrix representation. Our…
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…
We compute the full order statistics of a one-dimensional gas of fermions in a harmonic trap at zero temperature, including its large deviation tails. The problem amounts to computing the probability distribution of the $k$th smallest…
Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of…
We present a general model-independent formalism of measuring CP and CPT violating parameters through time-ordered integrated rates of correlated decays of $C=\pm 1$ entangled states of neutral pseudoscalar mesons. We give the general…
A perturbation decaying to 0 at infinity and not too irregular at 0 introduces at most a discrete set of eigenvalues into the spectral gaps of a one-dimensional Dirac operator on the half-line. We show that the number of these eigenvalues…
We study the limiting behavior of smooth linear statistics of the spectrum of random permutation matrices in the mesoscopic regime, when the permutation follows one of the Ewens measures on the symmetric group. If we apply a smooth enough…
We compute the exact and limiting smallest eigenvalue distributions for two classes of $\beta$-Jacobi ensembles not covered by previous studies. In the general $\beta$ case, these distributions are given by multivariate hypergeometric…
We investigate spacing statistics $p(s)$ and distribution of eigenvalues $D(\epsilon)$ for ensembles of various real random matrices (of order $n \times n, n=2$ and $n>>2$) where the matrix-elements have various Probability Distribution…
We present some applications of central limit theorems on mesoscopic scales for random matrices. When combined with the recent theory of "homogenization" for Dyson Brownian Motion, this yields the universality of quantities which depend on…
We compute spectra of sample auto-covariance matrices of second order stationary stochastic processes. We look at a limit in which both the matrix dimension $N$ and the sample size $M$ used to define empirical averages diverge, with their…
The eigenvalues for the minors of real symmetric ($\beta=1$) and complex Hermitian ($\beta=2$) Wigner matrices form the Wigner corner process, which is a multilevel interlacing particle system. In this paper, we study the microscopic…
The distribution of the ratios of consecutive eigenvalue spacings of random matrices has emerged as an important tool to study spectral properties of many-body systems. This article numerically investigates the eigenvalue ratios…
We present efficient numerical techniques for calculation of eigenvalue distributions of random matrices in the beta-ensembles. We compute histograms using direct simulations on very large matrices, by using tridiagonal matrices with…
We investigate the statistical properties of $C=uvu^{-1}v^{-1}$, when $u$ and $v$ are independent random matrices, uniformly distributed with respect to the Haar measure of the groups $U(N)$ and $O(N)$. An exact formula is derived for the…
This paper studies the delocalized regime of an ultrametric random operator whose independent entries have variances decaying in a suitable hierarchical metric on $\mathbb{N}$. When the decay-rate of the off-diagonal variances is…
We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…
We describe an ensemble of (sparse) random matrices whose eigenvalues follow the Gibbs distribution for n particles of the Coulomb gas on the unit circle at inverse temperature beta. Our approach combines elements from the theory of…