Uniform minorization condition and convergence bounds for discretizations of kinetic Langevin dynamics

Understand

We study the convergence in total variation and $V$-norm of discretization schemes of the underdamped Langevin dynamics.

• Such algorithms are very popular and commonly used in molecular dynamics and computational statistics to approximatively sample from a target distribution of interest.
• We show first that, for a very large class of schemes, a minorization condition uniform in the stepsize holds.
• This class encompasses popular methods such as the Euler-Maruyama scheme and the schemes based on splitting strategies.