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 $\mathbb{C}^n$.
Publié le : 2006-09-14
Classification:
$C^*$-algebra,
reductive homogeneous space,
lifting of geodesics,
exponential families,
maximum entropy method,
46L05,
53C05,
53C56,
60B99,
60E05,
53C30,
32M99,
62A25,
94A17
@article{1161871347,
author = {Gzyl
,
Henryk and Recht
,
L\'azaro},
title = {A geometry on the space of probabilities I. The finite dimensional case},
journal = {Rev. Mat. Iberoamericana},
volume = {22},
number = {2},
year = {2006},
pages = { 545-558},
language = {en},
url = {http://dml.mathdoc.fr/item/1161871347}
}
Gzyl
,
Henryk; Recht
,
Lázaro. A geometry on the space of probabilities I. The finite dimensional case. Rev. Mat. Iberoamericana, Tome 22 (2006) no. 2, pp. 545-558. http://gdmltest.u-ga.fr/item/1161871347/