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September, 2006 A geometry on the space of probabilities I. The finite dimensional case
Henryk Gzyl , Lázaro Recht
Rev. Mat. Iberoamericana 22(2): 545-558 (September, 2006).

Abstract

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 $\mathbb{C}^n$.

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Henryk Gzyl . Lázaro Recht . "A geometry on the space of probabilities I. The finite dimensional case." Rev. Mat. Iberoamericana 22 (2) 545 - 558, September, 2006.

Information

Published: September, 2006
First available in Project Euclid: 26 October 2006

zbMATH: 1121.46043
MathSciNet: MR2294789

Subjects:
Primary: 46L05 , 53C05 , 53C56 , 60B99 , 60E05
Secondary: 32M99 , 53C30 , 62A25 , 94A17

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

Rights: Copyright © 2006 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.22 • No. 2 • September, 2006
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