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.