Finite dimensional approximation of Riemannian path space geometry. (Q1421846)

The paper deals with the geometry of path space over a compact Riemannian manifold. The Riemannian geometry of this space in known to have many complicated features and difficulties, partly overcome previously by introducing the called Markovian connection (Riemannian with non-zero torsion). Here the authors construct a finite-dimensional approximation for path space based on finite partitions of the time interval that allows one to determine the horizontal lift of the Ornstein-Uhlenbeck processes through the Markovian connection as well as to prove a representation formula for the heat semigroup on adapted vector fields and a communication formula for its derivative.