JournalsrmiVol. 22, No. 2pp. 545–558

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

  • Henryk Gzyl

    Universidad Carlos III, Madrid-Getafe, Spain
  • Lázaro Recht

    Universidad Simón Bolívar, Caracas, Venezuela
A geometry on the space of probabilities I. The finite dimensional case cover
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Abstract

In this note we provide a natural way of defining exponential coordinates on the class of probabilities on the set Ω=[1,n]\Omega = [1,n] or on P={p=(p1,,pn)Rnpi>0;Σi=1npi=1}\mathbb{P} = \{p=(p_1,\dots,p_n)\in \mathbb{R}^n | p_i > 0; \Sigma_{i=1}^n p_i =1\}. For that we have to regard P\mathbb{P} as a projective space and the exponential coordinates will be related to geodesic flows in Cn\mathbb{C}^n.

Cite this article

Henryk Gzyl, Lázaro Recht, A geometry on the space of probabilities I. The finite dimensional case. Rev. Mat. Iberoam. 22 (2006), no. 2, pp. 545–558

DOI 10.4171/RMI/465