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<p>We prove the convergence of the spectrum of the generator of the kinetic Brownian motion to the spectrum of the base Laplacian for closed Riemannian manifolds. This generalizes recent work of Kolb–Weich–Wolf&#xa0;(Ann Henri Poincaré 23(4):1283–1296, 2022) on constant curvature surfaces and of Ren–Tao (Spectral asymptotics for kinetic brownian motion on locally symmetric spaces, 2022) on locally symmetric spaces. As an application, we prove a conjecture of Baudoin–Tardif (Kinetic Related Models 11(1):1–23, 2018) on the optimal convergence rate to the equilibrium.</p>

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Spectral asymptotics for kinetic Brownian motion on Riemannian manifolds

  • 期刊论文

  • 发表日期：

    2025年8月28日

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  • Qiuyu Ren,
  • Zhongkai Tao

摘要

We prove the convergence of the spectrum of the generator of the kinetic Brownian motion to the spectrum of the base Laplacian for closed Riemannian manifolds. This generalizes recent work of Kolb–Weich–Wolf (Ann Henri Poincaré 23(4):1283–1296, 2022) on constant curvature surfaces and of Ren–Tao (Spectral asymptotics for kinetic brownian motion on locally symmetric spaces, 2022) on locally symmetric spaces. As an application, we prove a conjecture of Baudoin–Tardif (Kinetic Related Models 11(1):1–23, 2018) on the optimal convergence rate to the equilibrium.