A probabilistic approach to heat diffusion on symmetric spaces
Let \(X\) be a Riemannian symmetric space of noncompact type. The asymptotic behaviour of Brownian motion is studied by using the Iwasawa decomposition of the Lie group which induces the horocyclic splittings of the homogeneous space. By discretization of time, the author gives new proofs for limit theorems in Iwasawa and Cartan decompositions. The final theorem shows that a result by Anker and Setti on asymptotic finite propagation speed for heat diffusion can be derived from the central limit theorem for the radial component of the Brownian motion.
scientific article; zbMATH DE number 637650
scientific article