Related papers: Statistics of Min-max Normalized Eigenvalues in Ra…

In this article, we establish a limiting distribution for eigenvalues of a class of auto-covariance matrices. The same distribution has been found in the literature for a regularized version of these auto-covariance matrices. The original…

Matrices with low-rank structure are ubiquitous in scientific computing. Choosing an appropriate rank is a key step in many computational algorithms that exploit low-rank structure. However, estimating the rank has been done largely in an…

We analyze gene co-expression network under the random matrix theory framework. The nearest neighbor spacing distribution of the adjacency matrix of this network follows Gaussian orthogonal statistics of random matrix theory (RMT). Spectral…

In this article, we study microscopic properties of a two-dimensional eigenvalue ensemble near a conical singularity arising from insertion of a point charge in the bulk of the support of eigenvalues. In particular, we characterize all…

A remarkable property of Hermitian ensembles is their universal behavior, that is, once properly rescaled the eigenvalue statistics does not depend on particularities of the ensemble. Recently, normal matrix ensembles have attracted…

Factor analysis, a classical multivariate statistical technique is popularly used as a fundamental tool for dimensionality reduction in statistics, econometrics and data science. Estimation is often carried out via the Maximum Likelihood…

The conventional rounding error analysis provides worst-case bounds with an associated failure probability and ignores the statistical property of the rounding errors. In this paper, we develop a new statistical rounding error analysis for…

We provide a statistical analysis of regularization-based continual learning on a sequence of linear regression tasks, with emphasis on how different regularization terms affect the model performance. We first derive the convergence rate…

In a paper that appeared in 2010, C. Tone proved a multivariate central limit theorem for some strictly stationary random fields of random vectors satisfying certain mixing conditions. The "normalization" of a given "partial sum" (or "block…

We propose a technique for calculating and understanding the eigenvalue distribution of sums of random matrices from the known distribution of the summands. The exact problem is formidably hard. One extreme approximation to the true density…

We consider the empirical eigenvalue distribution of an $m\times m$ principal submatrix of an $n\times n$ random unitary matrix distributed according to Haar measure. For $n$ and $m$ large with $\frac{m}{n}=\alpha$, the empirical spectral…

The muon optimizer has picked up much attention as of late as a possible replacement to the seemingly omnipresent Adam optimizer. Recently, care has been taken to document the scaling laws of hyper-parameters under muon such as weight decay…

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

We review the recent developments in the theory of normal, normal self-dual and general complex random matrices. The distribution and correlations of the eigenvalues at large scales are investigated in the large $N$ limit. The 1/N expansion…

Let $\bm{x}_1,\cdots,\bm{x}_n$ be a random sample of size $n$ from a $p$-dimensional population distribution, where $p=p(n)\rightarrow\infty$. Consider a symmetric matrix $W=X^\top X$ with parameters $n$ and $p$, where…

This paper studies the extreme gaps between eigenvalues of random matrices. We give the joint limiting law of the smallest gaps for Haar-distributed unitary matrices and matrices from the Gaussian unitary ensemble. In particular, the kth…

Triangular distributions are a well-known class of distributions that are often used as elementary example of a probability model. In the past, enumeration and order statistic-based methods have been suggested for the maximum likelihood…

Statistical properties of coherent radiation propagating in a quasi - 1D random media is studied in the framework of random matrix theory. Distribution functions for the total transmission coefficient and the angular transmission…

We develop an efficient algorithm for sampling the eigenvalues of random matrices distributed according to the Haar measure over the orthogonal or unitary group. Our technique samples directly a factorization of the Hessenberg form of such…

Scaling problems have a rich and diverse history, and thereby have found numerous applications in several fields of science and engineering. For instance, the matrix scaling problem has had applications ranging from theoretical computer…