Related papers: The Student ensemble of correlation matrices: eige…
Inferring and comparing complex, multivariable probability density functions is fundamental to problems in several fields, including probabilistic learning, network theory, and data analysis. Classification and prediction are the two faces…
This paper summarizes some work I've been doing on eigenvalue correlators of Random Matrix Models which show some interesting behaviour. First we consider matrix models with gaps in there spectrum or density of eigenvalues. The…
We prove that Kendall's Rank correlation matrix converges to the Mar\v{c}enko-Pastur law, under the assumption that the observations are i.i.d random vectors $X_1$, $\dots$, $X_n$ with components that are independent and absolutely…
We introduce a method for describing eigenvalue distributions of correlation matrices from multidimensional time series. Using our newly developed matrix H theory, we improve the description of eigenvalue spectra for empirical correlation…
We introduce a family of coefficients based on U-statistics that generalize the notion of correlation and explore their properties in the large dimensional multivariate case, showing that in the null case of uncorrelated variables, the…
Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical…
In statistics, assuming samples are independent is reasonable. However, this property can fail to hold for the features, a distinction that has led to several lines of work aiming to remove the latter assumption of independence present in…
Relative entropy serves as a cornerstone concept in quantum information theory. In this work, we study relative entropy of random states from major generic state models of Hilbert-Schmidt and Bures-Hall ensembles. In particular, we derive…
The entanglement spectrum, i.e., the full distribution of Schmidt eigenvalues of the reduced density matrix, contains more information than the conventional entanglement entropy and has been studied recently in several many-particle…
In this paper, we consider the empirical spectral distribution of the sample correlation matrix and investigate its asymptotic behavior under mild assumptions on the data's distribution, when dimension and sample size increase at the same…
This paper shows that large nonparametric classes of conditional multivariate densities can be approximated in the Kullback--Leibler distance by different specifications of finite mixtures of normal regressions in which normal means and…
We give an overview of the recursive characterisations of random matrix ensembles that are currently at the forefront of random matrix theory by way of studying two classes of ensembles using two different types of recursive schemes:…
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…
This work explores connections between the quantum relative entropy of two faithful states $\rho,\sigma$ (i.e. full-rank density matrices) and the Kullback-Leibler divergences of classical measures $\mu,\nu$. Here, $\mu$ and $\nu$ are…
An exact analytical description of extreme intensity statistics in complex random states is derived. These states have the statistical properties of the Gaussian and Circular Unitary Ensemble eigenstates of random matrix theory. Although…
The Kullback-Leibler cluster entropy $\mathcal{D_{C}}[P \| Q] $ is evaluated for the empirical and model probability distributions $P$ and $Q$ of the clusters formed in the realized volatility time series of five assets (SP\&500, NASDAQ,…
We investigate random density matrices obtained by partial tracing larger random pure states. We show that there is a strong connection between these random density matrices and the Wishart ensemble of random matrix theory. We provide…
We investigate the relation between the invariant correlators of random matrix theory and correlators of the integrable one-dimensional systems. Starting from the relation between correlators for the coupling strengths $\lambda =1/ 2$, $1$,…
We study the dependence of the spectral density of the covariance matrix ensemble on the power spectrum of the underlying multivariate signal. The white noise signal leads to the celebrated Marchenko-Pastur formula. We demonstrate results…
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…