A diffusion process associated with Fréchet means

This paper studies rescaled images, under exp.1., of the sample Fréchet means of i.i.d. random variables {Xk|k.1} with Fréchet mean . on a Riemannian manifold. We show that, with appropriate scaling, these images converge weakly to a diffusion process. Similar to the Euclidean case, this limiting diffusion is a Brownian motion up to a linear transformation. However, in addition to the covariance structure of exp.1.(X1), this linear transformation also depends on the global Riemannian structure of the manifold.