A uniform-in-time weakly convergent explicit numerical method for the underdamped Langevin equation with polynomial potentials (opens in new tab)

The underdamped Langevin equation is a fundamental model in statistical mechanics for sampling Gibbs measures and simulating molecular dynamics, for which numerical methods with uniform-in-time weak convergence are essential for accurately reproducing long-time statistical observables and invariant measures of the underlying dynamics. Currently, such uniform-in-time weak convergence is established for implicit schemes, but remains unknown for ex...