TY - JOUR
T1 - On the mean first arrival time of Brownian particles on Riemannian manifolds
AU - Nursultanov, Medet
AU - Tzou, Justin C.
AU - Tzou, Leo
PY - 2021/6
Y1 - 2021/6
N2 - 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 to treat this problem, which has thus far been limited to very special geometries. This paper can be seen as the Riemannian 3-manifold version of the planar result of [1] and thus enable us to see the full effect of the local extrinsic boundary geometry on the mean arrival time of the Brownian particles. Our approach also connects this question to some of the recent progress on boundary rigidity and integral geometry [21] and [18].
AB - 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 to treat this problem, which has thus far been limited to very special geometries. This paper can be seen as the Riemannian 3-manifold version of the planar result of [1] and thus enable us to see the full effect of the local extrinsic boundary geometry on the mean arrival time of the Brownian particles. Our approach also connects this question to some of the recent progress on boundary rigidity and integral geometry [21] and [18].
KW - Narrow escape problem
KW - Mean sojourn time
KW - Brownian motion
UR - http://purl.org/au-research/grants/arc/DP190103302
UR - http://purl.org/au-research/grants/arc/DP190103451
UR - http://www.scopus.com/inward/record.url?scp=85104668049&partnerID=8YFLogxK
U2 - 10.1016/j.matpur.2021.04.006
DO - 10.1016/j.matpur.2021.04.006
M3 - Article
VL - 150
SP - 202
EP - 240
JO - Journal de Mathématiques Pures et Appliquées
JF - Journal de Mathématiques Pures et Appliquées
SN - 0021-7824
ER -