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

Gzyl, Henryk, and Recht, Lázaro. "A geometry on the space of probabilities (I). The finite dimensional case.." Revista Matemática Iberoamericana 22.2 (2006): 545-558. <http://eudml.org/doc/41983>.

@article{Gzyl2006,
abstract = {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 &gt; 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.},
author = {Gzyl, Henryk, Recht, Lázaro},
journal = {Revista Matemática Iberoamericana},
keywords = {C*-álgebras; Espacios de probabilidad; Flujos geodésicos; Geometría diferencial global; -algebra; reductive homogeneous space; lifting of geodesics; exponential families; maximum entropy method},
language = {eng},
number = {2},
pages = {545-558},
title = {A geometry on the space of probabilities (I). The finite dimensional case.},
url = {http://eudml.org/doc/41983},
volume = {22},
year = {2006},
}

TY - JOUR
AU - Gzyl, Henryk
AU - Recht, Lázaro
TI - A geometry on the space of probabilities (I). The finite dimensional case.
JO - Revista Matemática Iberoamericana
PY - 2006
VL - 22
IS - 2
SP - 545
EP - 558
AB - 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 &gt; 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.
LA - eng
KW - C*-álgebras; Espacios de probabilidad; Flujos geodésicos; Geometría diferencial global; -algebra; reductive homogeneous space; lifting of geodesics; exponential families; maximum entropy method
UR - http://eudml.org/doc/41983
ER -