论文标题
在恒定曲率表面上动力学布朗运动的光谱渐近学
Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature
论文作者
论文摘要
Riemannian歧管$ M $的球体束上的动力学布朗运动是一个随机过程，它可以随机地扰动地球流动。如果$ m $是一种可以定位的紧凑型表面，我们表明，在无限大的扰动的极限中，该过程的无限发电机的$ l^2 $ - 光谱会收敛到基础歧管的拉普拉斯光谱。
The kinetic Brownian motion on the sphere bundle of a Riemannian manifold $M$ is a stochastic process that models a random perturbation of the geodesic flow. If $M$ is a orientable compact constantly curved surface, we show that in the limit of infinitely large perturbation the $L^2$-spectrum of the infinitesimal generator of a time rescaled version of the process converges to the Laplace spectrum of the base manifold.
