Fisher information metric and Poisson kernels |
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Authors: | Mitsuhiro Itoh Yuichi Shishido |
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Affiliation: | a Institute of Mathematics, University of Tsukuba, Tsukuba-city, Ibaraki, Japan, 305-8571 b Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba-city, Ibaraki, Japan, 305-8571 |
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Abstract: | A complete Riemannian manifold X with negative curvature satisfying −b2?KX?−a2<0 for some constants a,b, is naturally mapped in the space of probability measures on the ideal boundary ∂X by assigning the Poisson kernels. We show that this map is embedding and the pull-back metric of the Fisher information metric by this embedding coincides with the original metric of X up to constant provided X is a rank one symmetric space of non-compact type. Furthermore, we give a geometric meaning of the embedding. |
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Keywords: | 53C35 53C42 58B20 58J32 |
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