Central limit theorem on noncompact Riemannian symmetric spaces of rank one

IN 1994, Terras obtained the central limit theorem on Poincare upper half planeM=SL(2,R)/SO(2). This is the first non-Euclidean central limit theorem on a noncompactRiemannian symmetric space. Based on the spherical Follrier transform, using the expressionsof the heat kernel obtained by Lohoue et al. , we establish in this note the non-Euclideancentral limit theorem on noncompact Riemannian symmetric spaces of rank one.