Abstract We study the Unadjusted Langevin Algorithm (ULA) for sampling from a probability
distribution $\nu= e^{-f} $ on $\R^ n $. We prove a convergence guarantee in Kullback …

This paper is devoted to the study of propagation of chaos and mean-field limits for systems
of indistinguishable particles, undergoing collision processes. The prime examples we will …

We prove that if (P x) x∈ X is a family of probability measures which satisfy the log-Sobolev
inequality and whose pairwise chi-squared divergences are uniformly bounded, and μ is …

We consider a diffusion on a potential landscape which is given by a smooth Hamiltonian
H:R^n→R in the regime of low temperature ε. We proof the Eyring–Kramers formula for the …

The efficacy of modern generative models is commonly contingent upon the precision of
score estimation along the diffusion path, with a focus on diffusion models and their ability to …

This paper provides a general framework for Stein's density method for multivariate
continuous distributions. The approach associates to any probability density function a …

The aim of this paper is to establish various functional inequalities for the convolution of a
compactly supported measure and a standard Gaussian distribution on R^d. We especially …

To understand the training dynamics of neural networks (NNs), prior studies have
considered the infinite-width mean-field (MF) limit of two-layer NN, establishing theoretical …

We prove geometric upper bounds for the Poincaré and Logarithmic Sobolev constants for
Brownian motion on manifolds with sticky reflecting boundary diffusion ie extended Wentzell …

The primary contribution of this thesis is to advance the theory of complexity for sampling
from a continuous probability density over R^ d. Some highlights include: a new analysis of …