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

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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