Publications [#372698] of Jianfeng Lu

Papers Published

1. Cao, Y; Lu, J; Wang, L, On Explicit L² -Convergence Rate Estimate for Underdamped Langevin Dynamics, Archive for Rational Mechanics and Analysis, vol. 247 no. 5 (October, 2023) [doi]
   (last updated on 2024/11/20)

   Abstract:
   We provide a refined explicit estimate of the exponential decay rate of underdamped Langevin dynamics in the L2 distance, based on a framework developed in Albritton et al. (Variational methods for the kinetic Fokker–Planck equation, arXiv arXiv:1902.04037 , 2019). To achieve this, we first prove a Poincaré-type inequality with a Gibbs measure in space and a Gaussian measure in momentum. Our estimate provides a more explicit and simpler expression of the decay rate; moreover, when the potential is convex with a Poincaré constant m≪ 1 , our estimate shows the decay rate of O(m) after optimizing the choice of the friction coefficient, which is much faster than m for the overdamped Langevin dynamics.