A geometry on the space of probabilities. I: The finite dimensional case
Summary: We provide a natural way of defining exponential coordinates on the class of probabilities on the set \(\Omega = [1,n]\) or on \(\mathbb{P} = \{p=(p_1,\dots,p_n)\in \mathbb{R}^n \mid p_i > 0;\;\Sigma_{i=1}^n p_i =1\}\). For that, we have to regard \(\mathbb{P}\) as a projective space and the exponential coordinates will be related to geodesic flows in \(\mathbb{C}^n\). [Part II has appeared ibid.\ 22, No.\,3, 833--849 (2006; Zbl 1122.46039).]
scientific article; zbMATH DE number 5152582