The objective of molecular dynamics computations is to infer macroscopic properties of
matter from atomistic models via averages with respect to probability measures dictated by …

We consider ${\mathbb {R}}^ d $-valued diffusion processes of type\begin {align*} dX_t\=\b
(X_t) dt+ dB_t.\end {align*} Assuming a geometric drift condition, we establish contractions of …

There are many Markov chains on infinite dimensional spaces whose one-step transition
kernels are mutually singular when starting from different initial conditions. We give results …

We study the relationship between two classical approaches for quantitative ergodic
properties: the first one based on Lyapunov type controls and popularized by Meyn and …

The aim of this minicourse is to provide a number of tools that allow one to determine at
which speed (if at all) the law of a diffusion process, or indeed a rather general Markov …

A standard approach to computing expectations with respect to a given target measure is to
introduce an overdamped Langevin equation which is reversible with respect to the target …

In this article, we consider the problem of sampling from a probability measure π having a
density on R d proportional to x↦ e− U (x). The Euler discretization of the Langevin …

We consider multi-class systems of interacting nonlinear Hawkes processes modeling
several large families of neurons and study their mean field limits. As the total number of …

We establish subgeometric bounds on convergence rate of general Markov processes in the
Wasserstein metric. In the discrete time setting we prove that the Lyapunov drift condition …

We provide simple and constructive proofs of Harris-type theorems on the existence and
uniqueness of an equilibrium and the speed of equilibration of discrete-time and continuous …