On the Mean First Arrival Time of Brownian Particles on Riemannian Manifolds

摘要: Abstract We use geometric microlocal methods to compute an asymptotic expansion of mean first arrival time for Brownian particles on Riemannian manifolds. This approach provides a robust way treat this problem, which has thus far been limited very special geometries. paper can be seen as the 3-manifold version planar result [1] (Ammari, Kalimeris, Kang, and Lee; 2011) enable us see full effect local extrinsic boundary geometry particles. Our also connects question some recent progress rigidity integral [22] (Pestov Uhlmann; 2005) [19] (Monard, Nickl, Paternain; 2019).