论文标题
riemannian歧管上动力学布朗运动的光谱渐近学
Spectral asymptotics for kinetic Brownian motion on Riemannian manifolds
论文作者
论文摘要
我们证明了动力学布朗运动的发电机频谱与基础拉普拉斯基谱的频谱的融合，以封闭的riemannian歧管。这概括了KOLB - WEICH-沃尔夫[Arxiv：2011.06434]在恒定曲率表面和ren- -tao [arxiv：2208.13111]上的工作。作为一种应用，我们证明了baudoin--tardif [arxiv：1604.06813]的猜想对均衡的最佳收敛速率。
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 [arXiv:2011.06434] on constant curvature surfaces and of Ren--Tao [arXiv:2208.13111] on locally symmetric spaces. As an application, we prove a conjecture of Baudoin--Tardif [arXiv:1604.06813] on the optimal convergence rate to the equilibrium.
