Related papers: On Empirical Spectral Distributions for Random Ten…
We study the asymptotic of the spectral distribution for large empirical covariance matrices composed of independent Multifractal Random Walk processes. The asymptotic is taken as the observation lag shrinks to 0. In this setting, we show…
The Glivenko-Cantelli theorem states that the empirical distribution function converges uniformly almost surely to the theoretical distribution for a random variable $X \in \mathbb{R}$. This is an important result because it establishes the…
Let $\mathbf X=(X_{jk})_{j,k=1}^n$ denote a Hermitian random matrix with entries $X_{jk}$, which are independent for $1\le j\le k\le n$. We consider the rate of convergence of the empirical spectral distribution function of the matrix…
In practice, observations are often contaminated by noise, making the resulting sample covariance matrix a signal-plus-noise sample covariance matrix. Aiming to make inferences about the spectral distribution of the population covariance…
We prove a local law in the bulk of the spectrum for random Gram matrices $XX^*$, a generalization of sample covariance matrices, where $X$ is a large matrix with independent, centered entries with arbitrary variances. The limiting…
Random sampling of large Markov matrices with a tunable spectral gap, a nonuniform stationary distribution, and a nondegenerate limiting empirical spectral distribution (ESD) is useful. Fix $c>0$ and $p>0$. Let $A_n$ be the adjacency matrix…
The multivariate Kendall-$\tau$ statistic, denoted by $K_n$, plays a significant role in robust statistical analysis. This paper establishes the limiting properties of the empirical spectral distribution (ESD) of $K_n$. We demonstrate that…
The asymptotic behaviour of Linear Spectral Statistics (LSS) of the smoothed periodogram estimator of the spectral coherency matrix of a complex Gaussian high-dimensional time series $(\y_n)_{n \in \mathbb{Z}}$ with independent components…
In this paper we consider a new normalization of matrices obtained by choosing distinct codewords at random from linear codes over finite fields and find that under some natural algebraic conditions of the codes their empirical spectral…
Let $\{x_{\alpha}\}_{\alpha \in \mathbb{Z}}$ and $\{y_{\alpha}\}_{\alpha \in \mathbb{Z}}$ be two independent collections of zero mean, unit variance random variables with uniformly bounded moments of all orders. Consider a nonsymmetric…
In this paper we show that the empirical eigenvalue distribution of any sample covariance matrix generated by independent copies of a stationary regular sequence has a limiting distribution depending only on the spectral density of the…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
In random matrix theory, Marchenko-Pastur law states that random matrices with independent and identically distributed entries have a universal asymptotic eigenvalue distribution under large dimension limit, regardless of the choice of…
We investigate concentration properties of spectral measures of Hermitian random matrices with partially dependent entries. More precisely, let $X_n$ be a Hermitian random matrix of size $n\times n$ that can be split into independent blocks…
We analyze the empirical spectral distribution of random periodic band matrices with correlated entries. The correlation structure we study was first introduced in 2015 by Hochst\"attler, Kirsch and Warzel, who named their setup "almost…
In this paper we present the asymptotic theory for spectral distributions of high dimensional covariation matrices of Brownian diffusions. More specifically, we consider $N$-dimensional Ito integrals with time varying matrix-valued…
We define the empirical spectral distribution (ESD) of a random matrix polynomial with invertible leading coefficient, and we study it for complex $n \times n$ Gaussian monic matrix polynomials of degree $k$. We obtain exact formulae for…
Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…
Consider an $N$ by $N$ matrix $X$ of complex entries with iid real and imaginary parts. We show that the local density of eigenvalues of $X^*X$ converges to the Marchenko-Pastur law on the optimal scale with probability $1$. We also obtain…
We consider products of independent random matrices with independent entries. The limit distribution of the expected empirical distribution of eigenvalues of such products is computed. Let $X^{(\nu)}_{jk},{}1\le j,r\le n$, $\nu=1,...,m$ be…