Related papers: A Random Matrix Approach to VARMA Processes
Slow kinetic processes of molecular systems can be analyzed by computing dominant eigenpairs of the Koopman operator or its generator. In this context, the Variational Approach to Markov Processes (VAMP) provides a rigorous way of…
For a large Hermitian matrix $A\in \mathbb{C}^{N\times N}$, it is often the case that the only affordable operation is matrix-vector multiplication. In such case, randomized method is a powerful way to estimate the spectral density (or…
We provide a novel method for large volatility matrix prediction with high-frequency data by applying eigen-decomposition to daily realized volatility matrix estimators and capturing eigenvalue dynamics with ARMA models. Given a sequence of…
We compare eigenvalue densities of Wigner random matrices whose elements are independent identically distributed (iid) random numbers with a Levy distribution and maximally random matrices with a rotationally invariant measure exhibiting a…
This article studies the limiting behavior of a class of robust population covariance matrix estimators, originally due to Maronna in 1976, in the regime where both the number of available samples and the population size grow large. Using…
The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the…
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 review the ideas of how random matrix theory has to be properly applied to quantum physics; particularly we focus on how the spectrum has to be properly prepared and the random matrix correctly identified before the random matrix and the…
We present a quantum Monte Carlo method capable of sampling the full density matrix of a many-particle system at finite temperature. This allows arbitrary reduced density matrix elements and expectation values of complicated non-local…
High-frequency sampled multivariate continuous time autoregressive moving average processes are investigated. We obtain asymptotic expansion for the spectral density of the sampled MCARMA process $(Y_{n\Delta})_{n \in \mathbb{Z}}$ as…
Results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors. A common strategy to solve this problem is to estimate the…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
We consider the eigenvalues of sample covariance matrices of the form $\mathcal{Q}=(\Sigma^{1/2}X)(\Sigma^{1/2}X)^*$. The sample $X$ is an $M\times N$ rectangular random matrix with real independent entries and the population covariance…
Generating large-scale samples of stationary random fields is of great importance in the fields such as geomaterial modeling and uncertainty quantification. Traditional methodologies based on covariance matrix decomposition have the…
We extend to the matrix setting a recent result of Srivastava-Vershynin about estimating the covariance matrix of a random vector. The result can be in- terpreted as a quantified version of the law of large numbers for positive…
We introduce a random matrix model for the stationary covariance of multivariate Ornstein-Uhlenbeck processes with heterogeneous temperatures, where the covariance is constrained by the Sylvester-Lyapunov equation. Using the replica method,…
It recently has been found that methods of the statistical theories of spectra can be a useful tool in the analysis of spectra far from levels of Hamiltonian systems. Several examples originate from areas, such as quantitative linguistics…
The distribution of eigenvalues of N times N random matrices in the limit N to infinity is the solution to a variational principle that determines the ground state energy of a confined fluid of classical unit charges. This fact is a…
In dealing with high-dimensional data sets, factor models are often useful for dimension reduction. The estimation of factor models has been actively studied in various fields. In the first part of this paper, we present a new approach to…
We investigate the spectral distribution of large sample covariance matrices with independent columns and entries in the columns that stem from Markov chains. We characterize the limiting spectral densities by their moments.…