Revista Matemática Iberoamericana


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Volume 22, Issue 2, 2006, pp. 545–558
DOI: 10.4171/RMI/465

Published online: 2006-08-31

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

Henryk Gzyl[1] and Lázaro Recht[2]

(1) Universidad Carlos III, Madrid-Getafe, Spain
(2) Universidad Simón Bolívar, Caracas, Venezuela

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

Keywords: C*-algebra, reductive homogeneous space, lifting of geodesics, exponential families, maximum entropy method

Gzyl Henryk, Recht Lázaro: A geometry on the space of probabilities I. The finite dimensional case. Rev. Mat. Iberoam. 22 (2006), 545-558. doi: 10.4171/RMI/465