Related papers: Some Notes on Quantitative Generalized CLTs with S…
This paper deals with the estimation of a probability measure on the real line from data observed with an additive noise. We are interested in rates of convergence for the Wasserstein metric of order $p\geq 1$. The distribution of the…
The "typical" asymptotic behavior of the weighted sums of independent random vectors in $k$-dimensional space is considered. It is shown that in this case the rate of convergence in the multivariate central limit theorem is of order…
We establish a central limit theorem for the fluctuations of the linear statistics in the $\beta$-ensemble of dimension $N$ at a temperature proportional to $N$ and with confining smooth potential. In this regime, the particles do not…
It is well known that typical PT-symmetric systems suffer symmetry breaking when the strength of the gain-loss terms exceeds a certain critical value. We present a summary of recently published and newly produced results which demonstrate…
It is well known that central order statistics exhibit a central limit behavior and converge to a Gaussian distribution as the sample size grows. This paper strengthens this known result by establishing an entropic version of the CLT that…
Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance. The SGDCT algorithm…
The Central Limit Theorem (CLT) is one of the most fundamental results in statistics. It states that the standardized sample mean of a sequence of $n$ mutually independent and identically distributed random variables with finite first and…
This work focuses on the numerical approximations of neutral stochastic delay differential equations with their drift and diffusion coefficients growing super-linearly with respect to both delay variables and state variables. Under…
The paper establishes the strong convergence rates of a spatio-temporal full discretization of the stochastic wave equation with nonlinear damping in dimension one and two. We discretize the SPDE by applying a spectral Galerkin method in…
A new method of estimating population linear spectral statistics from high-dimensional data is introduced. When the dimension $d$ grows with the sample size $n$ such that $\frac{d}{n} \to c>0$, the proposed method is the first with proven…
Using the recently introduced time-local formulation of the nonequilibrium cluster perturbation theory (CPT), we construct a generalization of the approach such that macroscopic conservation laws are respected. This is achieved by…
The accurate and efficient computation of the deformation of crystalline solids requires the coupling of atomistic models near lattice defects such as cracks and dislocations with coarse-grained models away from the defects. Quasicontinuum…
We use here a particle system to prove a convergence result as well as a deviation inequality for solutions of granular media equation when the confinement potential and the interaction potential are no more uniformly convex. Proof is…
Consider an empirical measure $\mathbb{P}_n$ induced by $n$ iid samples from a $d$-dimensional $K$-subgaussian distribution $\mathbb{P}$ and let $\gamma = N(0,\sigma^2 I_d)$ be the isotropic Gaussian measure. We study the speed of…
The purpose of this paper is to provide a first class of explicit sufficient conditions for the central limit theorem and related results in the setup of non-uniformly (partially) expanding non iid random transformations, considered as…
Random hyperspherical harmonics are Gaussian Laplace eigenfunctions on the unit $d$-sphere ($d\ge 2$). We investigate the distribution of their defect i.e., the difference between the measure of positive and negative regions. Marinucci and…
We consider the spectral properties of a class of regularized estimators of (large) empirical covariance matrices corresponding to stationary (but not necessarily Gaussian) sequences, obtained by banding. We prove a law of large numbers…
We investigate the Wasserstein distance between the empirical spectral distribution of non-Hermitian random matrices and the Circular Law. For general entry distributions, we obtain a nearly optimal rate of convergence in 1-Wasserstein…
We consider deconvolution from repeated observations with unknown error distribution. So far, this model has mostly been studied under the additional assumption that the errors are symmetric. We construct an estimator for the non-symmetric…
We propose of an improved version of the ubiquitous symmetrization inequality making use of the Wasserstein distance between a measure and its reflection in order to quantify the symmetry of the given measure. An empirical bound on this…