Sharp hypocoercive convergence estimates for underdamped Langevin dynamics via the modified $L^2$ method

Zexi Fan, Bowen Li, Jianfeng Lu

In this note, we consider the underdamped Langevin dynamics with invariant measure $\mu (\mathrm{d}x\mathrm{d}v)\propto e^{-U(x)-|v{|}^2/2}\mathrm{d}x\mathrm{d}v$. Assume that th…