A note on the Fisher information metric and heat kernels

摘要: A heat kernel map is defined from a complete Riemannian manifold (X, h) into the space P (X) of probabilities on X whose density function is positive. By pulling back, by this heat kernel map, the Fisher information metric on it, we assert that this induced metric is homothetic to the original metric of X, provided (X, h) is a rank one symmetric space of non-compact type and, also discuss monotonicity of the homothety constant in time.AMS Subject Classification: 53C35, 53C42, 58B20