Abstract: |
In prior work of Andersson-Driver, the path space with finite interval over a compact Riemannian manifold is approximated by finite dimensional manifolds $H_{x,\P} (M)$ consisting of piecewise geodesic paths adapted to partitions $\P$ of $[0,T]$, and the associated Wiener measure is also approximated by a sequence of probability measures on finite dimensional manifolds. In this talk, we will discuss these approximations on general Riemannian path space (possibly with infinite interval) over a non-compact Riemannian manifold. Extension to the free path space. |