Related papers: Random Matrices with Slow Correlation Decay
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
Random correlation matrices are studied for both theoretical interestingness and importance for applications. The author of [6] is interested in their interpretation as covariance matrices of purely random signals, the authors of [16]…
We obtain estimates on the decay of correlations, Central Limit Theorem and Large Deviations for dynamical systems admitting an induced weak Gibbs--Markov map, for larger classes of observables with weaker regularity than H\"{o}lder,…
We consider random $n\times n$ matrices $X$ with independent and centered entries and a general variance profile. We show that the spectral radius of $X$ converges with very high probability to the square root of the spectral radius of the…
This work introduces the minimax Laplace transform method, a modification of the cumulant-based matrix Laplace transform method developed in "User-friendly tail bounds for sums of random matrices" (arXiv:1004.4389v6) that yields both upper…
In this paper, we study the empirical spectral distribution of Spearman's rank correlation matrices, under the assumption that the observations are independent and identically distributed random vectors and the features are correlated. We…
Improving upon results of Rudelson and Vershynin, we establish delocalization bounds for eigenvectors of independent-entry random matrices. In particular, we show that with high probability every eigenvector is delocalized, meaning any…
Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional data, particularly beyond the case of "null models" for which…
We study the eigenvectors of generalized Wigner matrices with subexponential entries and prove that they delocalize at the optimal rate with overwhelming probability. We also prove high probability delocalization bounds with sharp…
The analysis of diagonalizable matrices in terms of their so-called isospectral reduction represents a versatile approach to the underlying eigenvalue problem. Starting from a symmetry of the isospectral reduction, we show in the present…
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…
Some monotone increasing sequences of the lower bounds for the minimum eigenvalue of $M$-matrices are given. It is proved that these sequences are convergent and improve some existing results. Numerical examples show that these sequences…
We prove edge universality of local eigenvalue statistics for orthogonal invariant matrix models with real analytic potentials and one interval limiting spectrum. Our starting point is the result of \cite{S:08} on the representation of the…
This work presents numerical evidences that for discrete dynamical systems with one positive Lyapunov exponent the decay of the distance autocorrelation is always related to the Lyapunov exponent. Distinct decay laws for the distance…
In this paper, we use an adjusted autoencoder to estimate the true eigenvalues of the population correlation matrix from the sample correlation matrix when the number of samples is small. We show that the model outperforms the Rotational…
We study the convergence properties of a pair of learning algorithms (learning with and without memory). This leads us to study the dominant eigenvalue of a class of random matrices. This turns out to be related to the roots of the…
We are interested in investigating the statistical properties of extreme values for strongly correlated variables. The starting motivation is to understand how the strong-correlation properties of power-law distributed processes affect the…
We calculate analytically the probability of large deviations from its mean of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary and symplectic ensembles. In particular, we show that the…
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…
We consider the spectral radius of a large random matrix $X$ with independent, identically distributed entries. We show that its typical size is given by a precise three-term asymptotics with an optimal error term beyond the radius of the…