A geometry on the space of probabilities (I). The finite dimensional case.
Henryk Gzyl, Lázaro Recht (2006)
Revista Matemática Iberoamericana
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In this note we provide a natural way of defining exponential coordinates on the class of probabilities on the set Ω = [1,n] or on P = {p = (p, ..., p) ∈ R| p > 0; Σ p = 1}. For that we have to regard P as a projective space and the exponential coordinates will be related to geodesic flows in C.