Canonical Brownian Motion on the Diffeomorphism Group of the Circle

For infinitesimal data given on the group of diffeomorphism of the circle with respect to the metric H3/2, the associated Brownian motion has been constructed by Malliavin (C.R. Acad. Sci. Parist.329 (1999), 325–329). In this work, we shall give another approach and prove the invariance of heat measures under the adjoint action of S1.