相关论文: Spectral distribution of random matrices from Mutu…

This paper investigates limiting spectral distribution of a high-dimensional Kendall's rank correlation matrix. The underlying population is allowed to have general dependence structure. The result no longer follows the generalized…

We prove a law of large numbers for empirical approximations of the spectrum of a kernel integral operator by the spectrum of random matrices based on a sample drawn from a Markov chain, which complements the results by V. Koltchinskii and…

Distance matrices are matrices whose elements are the relative distances between points located on a certain manifold. In all cases considered here all their eigenvalues except one are non-positive. When the points are uncorrelated and…

It is well known that, under some assumptions, the limit distribution of random block matrices and their partial transposition converges to the distributions of random variables in some noncommutative probability space. Using free…

A non-Hermitean extension of paradigmatic Wishart random matrices is introduced to set up a theoretical framework for statistical analysis of (real, complex and real quaternion) stochastic time series representing two "remote" complex…

A new method of estimating population linear spectral statistics from high-dimensional data is introduced. When the dimension $d$ grows with the sample size $n$ such that $\frac{d}{n} \to c>0$, the proposed method is the first with proven…

Random matrix theory is finding an increasing number of applications in the context of information theory and communication systems, especially in studying the properties of complex networks. Such properties include short-term and long-term…

We investigate parameter identifiability of spectral distributions of random matrices. In particular, we treat compound Wishart type and signal-plus-noise type. We show that each model is identifiable up to some kind of rotation of…

We introduce a family of matrices with non-commutative entries that generalize the classical real Wishart matrices. With the help of the Brauer product, we derive a non-asymptotic expression for the moments of traces of monomials in such…

This paper considers the empirical spectral measure of a power of a random matrix drawn uniformly from one of the compact classical matrix groups. We give sharp bounds on the $L_p$-Wasserstein distances between this empirical measure and…

We study the eigenvalue distributions for sums of independent rank-one $k$-fold tensor products of large $n$-dimensional vectors. Previous results in the literature assume that $k=o(n)$ and show that the eigenvalue distributions converge to…

We show that a weak concentration property for quadratic forms of isotropic random vectors ${\bf x}$ is necessary and sufficient for the validity of the Marchenko-Pastur theorem for sample covariance matrices of random vectors having the…

The numerical algorithm of the inverse quantum scattering is developed. This algorithm is based on the Marchenko theory, and includes three steps. The first one is the algebraic Pade approximation of the unitary S-matrix, what is realized…

We show that the operatorial framework developed by Voiculescu for free random variables can be extended to arrays of random variables whose multiplication imitates matricial multiplication. The associated notion of independence, called…

We consider two different stationary random processes whose probability distributions are very close and indistinguishable by standard tests for large but limited statistics. Yet we demonstrate that these processes can be reliably…

We prove the Marchenko-Pastur theorem for random matrices with i.i.d. rows and a general dependence structure within the rows by a simple modification of the standard Cauchy-Stieltjes resolvent method.

Computing partition functions, the normalizing constants of probability distributions, is often hard. Variants of importance sampling give unbiased estimates of a normalizer Z, however, unbiased estimates of the reciprocal 1/Z are harder to…

We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…

A Markov tree is a random vector indexed by the nodes of a tree whose distribution is determined by the distributions of pairs of neighbouring variables and a list of conditional independence relations. Upon an assumption on the tails of…

The distribution of the consecutive level-spacing ratio is now widely used as a tool to distinguish integrable from chaotic quantum spectra, mostly due to its avoiding of the numerical spectral unfolding. Similar to the use of the…