Related papers: Correlation Matrix Spectra: A Tool for Detecting N…
We propose a two-sample test for high-dimensional means that requires neither distributional nor correlational assumptions, besides some weak conditions on the moments and tail properties of the elements in the random vectors. This…
Physics has been transforming our view of nature for centuries. While combining physical knowledge with computational approaches has enabled detailed modeling of physical systems' evolution, understanding the emergence of patterns and…
In data science, individual observations are often assumed to come independently from an underlying probability space. Kernel matrices formed from large sets of such observations arise frequently, for example during classification tasks. It…
We construct and analyze symmetrized delay correlation matrices for empirical data sets for atmopheric and financial data to derive information about correlation between different entities of the time series over time. The information about…
Power laws pervade statistical physics and complex systems, but, traditionally, researchers in these fields have paid little attention to properly fit these distributions. Who has not seen (or even shown) a log-log plot of a completely…
Several recent works have revealed a simplicity in equal-time correlators that is absent in their wavefunction counterparts. In this letter, we show that this arises from the simple fact that the correlator is obtained by integrating…
Given an optimization problem, the Hessian matrix and its eigenspectrum can be used in many ways, ranging from designing more efficient second-order algorithms to performing model analysis and regression diagnostics. When nonlinear models…
We extend classical time-frequency limiting analysis, historically applied to one-dimensional finite signals, to the multidimensional discrete setting. This extension is relevant for images, videos, and other multidimensional signals, as it…
We summarize properties of the spatial sign covariance matrix and especially look at the relationship between its eigenvalues and those of the shape matrix of an elliptical distribution. The explicit relationship known in the bivariate case…
A record is an entry in a time series that is larger or smaller than all previous entries. If the time series consists of independent, identically distributed random variables with a superimposed linear trend, record events are positively…
Extracting the three dimensional power spectrum from the 2D distribution of galaxies has become a standard tool of cosmology. This extraction requires some assumptions about the scaling of the power spectrum with redshift; all treatments to…
In the case where the dimension of the data grows at the same rate as the sample size we prove a central limit theorem for the difference of a linear spectral statistic of the sample covariance and a linear spectral statistic of the matrix…
In this paper we study an ensemble of random matrices called Elliptic Volatility Model, which arises in finance as models of stock returns. This model consists of a product of independent matrices $X = \Sigma Z $ where $Z$ is a $T$ by $S$…
We study various matrix models with a charge-charge interaction as toy models of the gauge dual of the AdS black hole. These models show a continuous spectrum and power-law decay of correlators at late time and infinite N, implying…
We analyze statistical properties of complex eigenvalues of random matrices $\hat{A}$ close to unitary. Such matrices appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with…
We construct a correlation matrix based financial network for a set of New York Stock Exchange (NYSE) traded stocks with stocks corresponding to nodes and the links between them added one after the other, according to the strength of the…
We present an empirical study in the geometric task of learning interatomic potentials, which shows equivariance matters even more at larger scales; we show a clear power-law scaling behaviour with respect to data, parameters and compute…
We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay…
Correlation function of complex eigenvalues of N by N random matrices drawn from non-Hermitean random matrix ensemble of symplectic symmetry is given in terms of a quaternion determinant. Spectral properties of Gaussian ensembles are…
Spectral hypergraph theory has recently attracted considerable interest as it provides a natural framework for modeling higher-order relationships beyond classical graphs. In this setting, eigenvalues of adjacency, Laplacian, and…