We introduce a framework to derive quantitative central limit theorems in the context of non-
linear approximation of Gaussian random variables taking values in a separable Hilbert …

Initiated around the year 2007, the Malliavin–Stein approach to probabilistic approximations
combines Stein's method with infinite-dimensional integration by parts formulae based on …

The Kolmogorov and total variation distance between the laws of random variables have
upper bounds represented by the L 1-norm of densities when random variables have …

We derive an upper bound on a probabilistic distance for a normal approximation when the
chaos grade of an eigenfunction of Markov diffusion generator L is greater than 2. When a …

In the case where the square of an eigenfunction F with respect to an eigenvalue of Markov
generator L can be expressed as a sum of eigenfunctions, we find the largest number …

We prove a quantitative functional central limit theorem for one-hidden-layer neural
networks with generic activation function. Our rates of convergence depend heavily on the …

We establish the convergence of the densities of a sequence of nonlinear functionals of an
underlying Gaussian process to the density of a Gamma distribution. We provide precise …

Initiated around the year 2007, the Malliavin-Stein approach to probabilistic approximations
combines Stein's method with infinite-dimensional integration by parts formulae based on …

This thesis contains two main chapters. The first chapter focuses on the highdimensional
asymptotic regimes of correlated Wishart matrices d− 1 𝒴𝒴 T, where 𝒴 is an× d Gaussian …

In this paper, we consider a quantitative fourth moment theorem for functions (random
variables) defined on the Markov triple (E, μ, Γ), where μ is a probability measure and Γ is …