The heat kernel measure Î¼t is constructed on GL(H), the group of invertible operators on a complex Hilbert space H. This measure is determined by an infinite dimensional Lie algebra g and a Hermitianâ€¦ (More)

The heat kernel measure Î¼t is constructed on an infinite dimensional complex group using a diffusion in a Hilbert space. Then it is proved that holomorphic polynomials on the group are squareâ€¦ (More)

A notion of the heat kernel measure is introduced for the L2 completion of a hyperfinite II1-factor with respect to the trace. Some properties of this measure are derived from the correspondingâ€¦ (More)

We give a new proof of the well-known fact that the pinned Wiener measure on a Lie group is quasi-invariant under right multiplication by 1nite energy paths. The main technique we use is the timeâ€¦ (More)

We consider different sub-Laplacians on a sub-Riemannian manifold M . Namely, we compare different natural choices for such operators, and give conditions under which they coincide. One of theseâ€¦ (More)

This paper considers a classical question of approximation of Brownian motion by a random walk in the setting of a sub-Riemannian manifold M . To construct such a random walk we first address severalâ€¦ (More)

We introduce a class of non-commutative Heisenberg-like infinite-dimensional Lie groups based on an abstract Wiener space. The Ricci curvature tensor for these groups is computed and shown to beâ€¦ (More)

We describe the exponential map from an infinite-dimensional Lie algebra to an infinite-dimensional group of operators on a Hilbert space. Notions of differential geometry are introduced for theseâ€¦ (More)

A further study of Riemannian geometry Diff(S1)/S1 is presented. We describe Hermitian and Riemannian metrics on the complexification of the homogeneous space, as well as the complexified symplecticâ€¦ (More)