Introduces a statistical model on complex domains via probability measures, derives a covariance-based curvature formula for the Bergman metric, proves a biholomorphism criterion from metric preservation, and establishes consistency plus CLT for the Fréchet mean of Calabi's diastasis.
Loi, A Laplace integral on a K¨ ahler manifold and Calabi’s diasta sis function , Differential Ge- ometry and its Applications 23 (2005), no
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Statistical Bergman geometry
Introduces a statistical model on complex domains via probability measures, derives a covariance-based curvature formula for the Bergman metric, proves a biholomorphism criterion from metric preservation, and establishes consistency plus CLT for the Fréchet mean of Calabi's diastasis.