Fisher information metric and Poisson kernels

DOI10.1016/j.difgeo.2007.11.027zbMath1144.53062OpenAlexW2003200245WikidataQ56287900 ScholiaQ56287900MaRDI QIDQ931142

Mitsuhiro Itoh, Yuichi Shishido

Publication date: 25 June 2008

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://tsukuba.repo.nii.ac.jp?action=repository_uri&item_id=16749

zbMATH Keywords

Poisson kernelFisher information metricminimal embeddingrank one symmetric space of non-compact type

Mathematics Subject Classification ID

Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Differential geometry of symmetric spaces (53C35) Boundary value problems on manifolds (58J32) Statistical aspects of information-theoretic topics (62B10)

Related Items (6)

Geometric mean of probability measures and geodesics of Fisher information metric ⋮ Fisher information geometry, Poisson kernel and asymptotical harmonicity ⋮ Information geometry of Poisson kernels on Damek-Ricci spaces ⋮ Information geometry of Busemann-barycenter for probability measures ⋮ Information geometry of the space of probability measures and barycenter maps ⋮ Horospheres and hyperbolicity of Hadamard manifolds

Cites Work

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• Entropy and rigidity of locally symmetric spaces of strictly negative curvature
• The dirichlet problem for the bergman laplacian. I
• Die Fisher-Information und symplektische Strukturen
• A note on the Poisson structures of the space of probability measures
• Compactifications of symmetric spaces

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