Entropy of Bergman measures of a toric Kaehler manifold

Abstract

Associated to the Bergman kernels of a polarized toric Kaehler manifold $(M,\omega ,L,h)$ are sequences of measures $\{{\mu }_k^z{\}}_{k=1}^{\infty }$ parametrized by the points $z\in M$. We determine the asymptotics of the entropies $H({\mu }_k^z)$ of these measures. The sequence ${\mu }_k^z$ in some ways resembles a sequence of convolution powers; we determine precisely when it actually is such a sequence.

Added results in the Fano case and especially in the Kahler-Einstein Fano case. Added an additional result on convolutions

References in corpus (1)

• Central Limit theorem for toric \kahler manifolds

Cited by in corpus (1)

• Expected centre of mass of the random Kodaira embedding