Related papers: A CLT for a band matrix model

We introduce a class of Boltzmann equations on the real line, which constitute extensions of the classical Kac caricature. The collisional gain operators are defined by smoothing transformations with quite general properties. By…

In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal…

This paper studies the asymptotic spectral properties of a renormalized sample correlation matrix, including the limiting spectral distribution, the properties of largest eigenvalues, and the central limit theorem for linear spectral…

Spectral measures of Wigner matrices are investigated. The Wigner semicircle law for spectral measures is proved. Regard this as the law of large number, the central limit theorem for moments spectral measure is also derived. The proof is…

We prove a Central Limit Theorem (CLT) in the non-commutative setting of random matrix products where the underlying process is driven by a subshift of finite type (SFT) with Markov measure. We use the martingale method introduced by Y.…

A non-classical formulation of the central limit theorem is given for sequences of independent random variables with finite second moments. Singular sequences whose members all have a degenerate or normal distribution are excluded from…

Central limit theorems (CLTs) for high-dimensional random vectors with dimension possibly growing with the sample size have received a lot of attention in the recent times. Chernozhukov et al. (2017) proved a Berry--Esseen type result for…

In this paper, we study the complex Wigner matrices $M_n=\frac{1}{\sqrt{n}}W_n$ whose eigenvalues are typically in the interval $[-2,2]$. Let $\lambda_1\leq \lambda_2...\leq\lambda_n$ be the ordered eigenvalues of $M_n$. Under the…

An equation is obtained for the Stieltjes transform of the normalized distribution of singular values of non-symmetric band random matrices in the limit when the band width and rank of the matrix simultaneously tend to infinity. Conditions…

Consider random symmetric Toeplitz matrices $T_{n}=(a_{i-j})_{i,j=1}^{n}$ with matrix entries $a_{j}, j=0,1,2,...,$ being independent real random variables such that \be \mathbb{E}[a_{j}]=0, \ \ \mathbb{E}[|a_{j}|^{2}]=1 \ \ \textrm{for}\,\…

We derive a strong law of large numbers, a central limit theorem, a law of the iterated logarithm and a large deviation theorem for so-called deviation means of independent and identically distributed random variables (for the strong law of…

We study the Central Limit Theorem (CLT) in the so-called hybrid Lebesgue-continuous spaces and tail behavior of normed sums of centered random independent variables (vectors) with values in these spaces.

In our previous paper \cite{FTD1}, we derived the almost sure convergence of the global density of eigenvalues of random matrices of the SYK model. In this paper, we will prove the central limit theorem for the linear statistic of…

We present a central limit theorem for stationary random fields that are short-range dependent and asymptotically independent. As an application, we present a central limit theorem for an infinite family of interacting It\^o-type diffusion…

In this paper, we rigorously derive Central Limit Theorems (CLT) for Bayesian two-layerneural networks in the infinite-width limit and trained by variational inference on a regression task. The different networks are trained via different…

We prove the Central Limit Theorem (CLT) from the definition of weak convergence using the Haar wavelet basis, calculus, and elementary probability. The use of the Haar basis pinpoints the role of $L^{2}([0,1])$ in the CLT as well as the…

We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal…

We develop a new toolbox for the analysis of the global behavior of stochastic discrete particle systems. We introduce and study the notion of the Schur generating function of a random discrete configuration. Our main result provides a…

We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem (LCLT) for non-autonomous dynamical systems. A key advance is the extension of the spectral…

Using the Coulomb Fluid method, this paper derives central limit theorems (CLTs) for linear spectral statistics of three "spiked" Hermitian random matrix ensembles. These include Johnstone's spiked model (i.e., central Wishart with spiked…