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On explicit $L^2$-convergence rate estimate for underdamped Langevin dynamics

Publication ,  Journal Article
Cao, Y; Lu, J; Wang, L
Published in: Arch Rational Mech Anal
August 13, 2019

We provide a refined explicit estimate of exponential decay rate of underdamped Langevin dynamics in $L^2$ distance, based on a framework developed in [1]. To achieve this, we first prove a Poincar\'{e}-type inequality with Gibbs measure in space and Gaussian measure in momentum. Our estimate provides a more explicit and simpler expression of decay rate; moreover, when the potential is convex with Poincar\'{e} constant $m \ll 1$, our estimate shows the decay rate of $O(\sqrt{m})$ after optimizing the choice of friction coefficient, which is much faster than $m$ for the overdamped Langevi dynamics.

Duke Scholars

Published In

Arch Rational Mech Anal

Publication Date

August 13, 2019

Volume

247

Start / End Page

90
 

Citation

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Cao, Y., Lu, J., & Wang, L. (2019). On explicit $L^2$-convergence rate estimate for underdamped Langevin dynamics. Arch Rational Mech Anal, 247, 90.
Cao, Yu, Jianfeng Lu, and Lihan Wang. “On explicit $L^2$-convergence rate estimate for underdamped Langevin dynamics.” Arch Rational Mech Anal 247 (August 13, 2019): 90.
Cao Y, Lu J, Wang L. On explicit $L^2$-convergence rate estimate for underdamped Langevin dynamics. Arch Rational Mech Anal. 2019 Aug 13;247:90.
Cao, Yu, et al. “On explicit $L^2$-convergence rate estimate for underdamped Langevin dynamics.” Arch Rational Mech Anal, vol. 247, Aug. 2019, p. 90.
Cao Y, Lu J, Wang L. On explicit $L^2$-convergence rate estimate for underdamped Langevin dynamics. Arch Rational Mech Anal. 2019 Aug 13;247:90.

Published In

Arch Rational Mech Anal

Publication Date

August 13, 2019

Volume

247

Start / End Page

90