Related papers: High-dimensional Central Limit Theorems by Stein's…
We study the normalized eigenvalue counting measure d\sigma of matrices of long-range percolation model. These are (2n+1)\times (2n+1) random real symmetric matrices H=\{H(i,j)\}_{i,j} whose elements are independent random variables taking…
The classical Berry-Esseen error bound, for the normal approximation to the law of a sum of independent and identically distributed random variables, is here improved by replacing the standardised third absolute moment by a weak norm…
We investigate the limiting behavior of sample central moments, examining the special cases where the limiting (as the sample size tends to infinity) distribution is degenerate. Parent (non-degenerate) distributions with this property are…
We derive a Gaussian Central Limit Theorem for the sample quantiles based on locally dependent random variables with explicit convergence rate. Our approach is based on converting the problem to a sum of indicator random variables, applying…
We study the central limit theorem in the non-normal domain of attraction to symmetric $\alpha$-stable laws for $0<\alpha\leq2$. We show that for i.i.d. random variables $X_i$, the convergence rate in $L^\infty$ of both the densities and…
Spectra of the degenerate two-photon absorption coefficient $\beta(\omega)$, anisotropy parameter $\sigma(\omega)$, and dichroism parameter $\delta(\omega) = \big[\sigma(\omega) + 2\eta(\omega)\big]/2$ of crystalline 110-cut GaAs, GaP, and…
The classical Perceptron algorithm of Rosenblatt can be used to find a linear threshold function to correctly classify $n$ linearly separable data points, assuming the classes are separated by some margin $\gamma > 0$. A foundational result…
Approximating the solution of the nonlinear filtering problem with Gaussian mixtures has been a very popular method since the 1970s. However, the vast majority of such approximations are introduced in an ad-hoc manner without theoretical…
In this paper, the optimal convergence rate $O\left(N^{-1/2}\right)$ (where $N$ is the total number of iterations performed by the algorithm), without the presence of a logarithmic factor, is proved for mirror descent algorithms with…
The problem of convergence of moments of a sequence of random variables to the moments of its asymptotic distribution is important in many applications. These include the determination of the optimal training sample size in the cross…
We consider the problem of identifying the parameters of an unknown mixture of two arbitrary $d$-dimensional gaussians from a sequence of independent random samples. Our main results are upper and lower bounds giving a computationally…
Ostrogradsky theorem states that Hamiltonian is unbounded when Euler-Lagrange equations are higher than second-order differential equations under the nondegeneracy assumption. Since higher-order nondegenerate Lagrangian can be always recast…
We give some rates of convergence in the distances of Kolmogorov and Wasserstein for standardized martingales with differences having finite variances. For the Kolmogorov distances, we present some exact Berry-Esseen bounds for martingales,…
We provide a Lyapunov type bound in the multivariate central limit theorem for sums of independent, but not necessarily identically distributed random vectors. The error in the normal approximation is estimated for certain classes of sets,…
A recent line of works, initiated by Russo and Xu, has shown that the generalization error of a learning algorithm can be upper bounded by information measures. In most of the relevant works, the convergence rate of the expected…
We consider the problem of digitalizing Euclidean segments. Specifically, we look for a constructive method to connect any two points in $\mathbb{Z}^d$. The construction must be {\em consistent} (that is, satisfy the natural extension of…
his study presents a novel technique to estimate the computational complexity of sequential decoding using the Berry-Esseen theorem. Unlike the theoretical bounds determined by the conventional central limit theorem argument, which often…
We obtain bounds to quantify the distributional approximation in the delta method for vector statistics (the sample mean of $n$ independent random vectors) for normal and non-normal limits, measured using smooth test functions. For normal…
The study of Dense-$3$-Subhypergraph problem was initiated in Chlamt{\'{a}}c et al. [Approx'16]. The input is a universe $U$ and collection ${\cal S}$ of subsets of $U$, each of size $3$, and a number $k$. The goal is to choose a set $W$ of…
In this paper, we derive a central limit theorem for collections of weakly correlated random variables indexed by discrete metric spaces, where the correlation decays in the distance of the indices. The correlation structure we study…