On non-Euclidean harmonic measure (Q2266275)

On an n-dimensional Riemannian manifold the Brownian motion process with infinitesimal generator the Laplace Beltrami operator is considered. According to the Onsager-Machlup formula the ''most probable path'' is that of a classical particle in a conservative force field whose potential is 1/12 the scalar curvature. This is made precise for surfaces in terms of the harmonic measure of a small geodesic sphere. The technique follows \textit{A. Gray} and \textit{M. A. Pinsky} [Bull. Sci. Math., II. Sér. 107, 345-370 (1983; Zbl 0522.58048)].