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A geometry on the space of probabilities (I). The finite dimensional case.

Henryk Gzyl, Lázaro Recht (2006)

Revista Matemática Iberoamericana

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 = (p1, ..., pn) ∈ Rn| pi > 0; Σi=1n pi = 1}. For that we have to regard P as a projective space and the exponential coordinates will be related to geodesic flows in Cn.

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