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Geometric Quantization of Complex Monge-Ampère Operator for Certain Diffusion Flows

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Geometric Science of Information (GSI 2013)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 8085))

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Abstract

In the 40’s, C.R. Rao considered probability distributions for a statistical model as the points of a Riemannian smooth manifold, where the considered Riemannian metric is the so-called Fisher metric. When extended to the complex projective space, this metric is actually the Fubini-Study metric. For certain models, it is quite remarkable that one actually needs to consider data with complex values.

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Author information

Authors and Affiliations

  1. Laboratoire d’Analyse Topologie et Probabilités, C.M.I, Aix-Marseille Université, France

    Julien Keller

Authors
  1. Julien Keller
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Editor information

Editors and Affiliations

  1. Sony Computer Science Laboratories Inc, Tokyo, Japan

    Frank Nielsen

  2. Thales Land Air Systems, 91470, Limours, France

    Frédéric Barbaresco

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Keller, J. (2013). Geometric Quantization of Complex Monge-Ampère Operator for Certain Diffusion Flows. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2013. Lecture Notes in Computer Science, vol 8085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40020-9_68

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  • DOI: https://doi.org/10.1007/978-3-642-40020-9_68

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40019-3

  • Online ISBN: 978-3-642-40020-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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