相关论文: Scaling in the eigenvalue fluctuations of the empi…

In this paper we study the distribution of the scaled largest eigenvalue of complexWishart matrices, which has diverse applications both in statistics and wireless communications. Exact expressions, valid for any matrix dimensions, have…

Let A be a p-variate real Wishart matrix on n degrees of freedom with identity covariance. The distribution of the largest eigenvalue in A has important applications in multivariate statistics. Consider the asymptotics when p grows in…

We investigate how in complex systems the eigenpairs of the matrices derived from the correlations of multichannel observations reflect the cluster structure of the underlying networks. For this we use daily return data from the NYSE and…

The variance--covariance matrix plays a central role in the inferential theories of high-dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many…

The cross correlation matrix between equities comprises multiple interactions between traders with varying strategies and time horizons. In this paper, we use the Maximum Overlap Discrete Wavelet Transform to calculate correlation matrices…

We present a Gaussian ensemble of random cyclic matrices on the real field and study their spectral fluctuations. These cyclic matrices are shown to be pseudo-symmetric with respect to generalized parity. We calculate the joint probability…

In this paper, we derive the explicit series expansion of the eigenvalue distribution of various models, namely the case of non-central Wishart distributions, as well as correlated zero mean Wishart distributions. The tools used extend…

Higher-order spacing ratios are investigated analytically using a Wigner-like surmise for Gaussian ensembles of random matrices. For $k$-th order spacing ratio $(r^{(k)}$, $k>1)$ the matrix of dimension $2k+1$ is considered. A universal…

WISDoM (Wishart Distributed Matrices) is a new framework for the quantification of deviation of symmetric positive-definite matrices associated to experimental samples, like covariance or correlation matrices, from expected ones governed by…

In the present work, eigenvalue distributions defined by a random rectangular matrix whose components are neither independently nor identically distributed are analyzed using replica analysis and belief propagation. In particular, we…

We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…

The aim of this note is to provide a pedagogical survey of the recent works by the authors ( arXiv:1409.7548 and arXiv:1507.06013) concerning the local behavior of the eigenvalues of large complex correlated Wishart matrices at the edges…

This paper develops on-line inference for the multivariate local level model, with the focus being placed on covariance estimation of the innovations. We assess the application of the inverse Wishart prior distribution in this context and…

We obtain general, exact formulas for the overlaps between the eigenvectors of large correlated random matrices, with additive or multiplicative noise. These results have potential applications in many different contexts, from quantum…

When dealing with non-stationary systems, for which many time series are available, it is common to divide time in epochs, i.e. smaller time intervals and deal with short time series in the hope to have some form of approximate stationarity…

Data sets collected at different times and different observing points can possess correlations at different times $and$ at different positions. The doubly correlated Wishart model takes both into account. We calculate the eigenvalue density…

Wishart correlation matrices are the standard model for the statistical analysis of time series. The ensemble averaged eigenvalue density is of considerable practical and theoretical interest. For complex time series and correlation…

Covariance matrices provide a valuable source of information about complex interactions and dependencies within the data. However, from a clustering perspective, this information has often been underutilized and overlooked. Indeed, commonly…

Motivated by differential co-expression analysis in genomics, we consider in this paper estimation and testing of high-dimensional differential correlation matrices. An adaptive thresholding procedure is introduced and theoretical…

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…