Information Geometry of Barycenter Map

  • Mitsuhiro Itoh
  • Hiroyasu Satoh
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 106)


Using barycenter of the Busemann function we define a map, called the barycenter map from a space \(\mathcal{P}^{+}\) of probability measures on the ideal boundary ∂ X to an Hadamard manifold X. We show that the space \(\mathcal{P}^{+}\) carries a fibre space structure over X from a viewpoint of information geometry. Following the idea of [7, 9] and [8] we present moreover a theorem which states that under certain hypotheses of information geometry a homeomorphism Φ of ∂ X induces, via the push-forward for probability measures, an isometry of X whose ∂ X-extension coincides with Φ.


Probability Measure Poisson Kernel Ideal Boundary Fibre Space Information Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors express their congratulatory address to Professor Young Jin Suh being selected as one of distinguished present mathematicians in Korea and the first author also is grateful to the organizing committee of ICMRCS2014, especially to Professor Suh.


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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of TsukubaTsukubaJapan
  2. 2.Nippon Institute of TechnologySaitamaJapan

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