Related papers: Optimal Bounds in Normal Approximation for Many In…

We establish upper and lower bounds for the expected Wasserstein distance between the random empirical measure and the uniform measure on the Boolean cube. Our analysis leverages techniques from Fourier analysis, following the framework…

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…

New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the Chen-Stein method. The new bounds rely on…

New bounds for the $k$-th order derivatives of the solutions of the normal and multivariate normal Stein equations are obtained. Our general order bounds involve fewer derivatives of the test function than those in the existing literature.…

For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…

This work introduces a new, explicit bound on the Hellinger distance between a continuous random variable and a Gaussian with matching mean and variance. As example applications, we derive a quantitative Hellinger central limit theorem and…

We propose a variational approach to approximate measures with measures uniformly distributed over a 1 dimentional set. The problem consists in minimizing a Wasserstein distance as a data term with a regularization given by the length of…

We establish explicit bounds on the convex distance between the distribution of a vector of smooth functionals of a Gaussian field, and that of a normal vector with a positive definite covariance matrix. Our bounds are commensurate to the…

Consider a stationary, weakly dependent sequence of random variables. Given only mild conditions, allowing for polynomial decay of the autocovariance function, we show a Berry-Esseen bound of optimal order $n^{-1/2}$ for studentized…

Let $n \in \mathbb N$, let $\zeta_{n,1},...,\zeta_{n,n}$ be a sequence of independent random variables with $\mathbb E \zeta_{n,i}=0$ and $\mathbb E |\zeta_{n,i}|<\infty$ for each $i$, and let $\mu$ be an $\alpha$-stable distribution having…

In this paper, we consider a target random variable $Y \sim \CVG$ distributed according to a centered Variance--Gamma distribution. For a generic random element $F=I_2(f)$ in the second Wiener chaos with $\E[F^2]= \E[Y^2]$ we establish a…

Distinguishing quantum states with minimal sampling overhead is of fundamental importance to teach quantum data to an algorithm. Recently, the quantum Wasserstein distance emerged from the theory of quantum optimal transport as a promising…

We introduce a new class of Wasserstein-type distances specifically designed to tackle questions concerning stability and convergence to equilibria for kinetic equations. Thanks to these new distances, we improve some classical estimates by…

We consider a mean-field control problem in which admissible controls are required to be adapted to the common noise filtration. The main objective is to show how the mean-field control problem can be approximates by time consistent…

In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical measure in the law of large numbers, in Wasserstein distance. We also consider occupation measures of ergodic Markov chains. One motivation…

We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…

We develop quantitative algorithmic information bounds for orthogonal projections and distances in the plane. Under mild independence conditions, the distance $|x-y|$ and a projection coordinate $p_e x$ each retain at least half the…

We establish both uniform and nonuniform error bounds of the Berry-Esseen type in normal approximation under local dependence. These results are of an order close to the best possible if not best possible. They are more general or sharper…

We study the convergence to equilibrium of the mean field PDE associated with the derivative-free methodologies for solving inverse problems. We show stability estimates in the euclidean Wasserstein distance for the mean field PDE by using…

We establish an explicit rate of convergence for some systems of mean-field interacting diffusions with logistic binary branching towards the solutions of nonlinear evolution equations with non-local self-diffusion and logistic mass growth,…