Abstract
Partial Bergman kernels are kernels of orthogonal projections onto subspaces of holomorphic sections of the power of an ample line bundle over a Kähler manifold . The subspaces of this article are spectral subspaces of the Toeplitz quantization of a smooth Hamiltonian . It is shown that the relative partial density of states satisfies where . Moreover it is shown that this partial density of states exhibits “Erf” asymptotics along the interface ; that is, the density profile asymptotically has a Gaussian error function shape interpolating between the values and of . Such “Erf” asymptotics are a universal edge effect. The different types of scaling asymptotics are reminiscent of the law of large numbers and the central limit theorem.
Citation
Steve Zelditch. Peng Zhou. "Central limit theorem for spectral partial Bergman kernels." Geom. Topol. 23 (4) 1961 - 2004, 2019. https://doi.org/10.2140/gt.2019.23.1961
Information