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

Revista Matemática Iberoamericana (2006)

- Volume: 22, Issue: 2, page 545-558
- ISSN: 0213-2230

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topGzyl, 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 > 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 > 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 -

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