Geometry & Topology
- Geom. Topol.
- Volume 23, Number 4 (2019), 1961-2004.
Central limit theorem for spectral partial Bergman kernels
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.
Geom. Topol., Volume 23, Number 4 (2019), 1961-2004.
Received: 30 August 2017
Revised: 17 April 2018
Accepted: 30 September 2018
First available in Project Euclid: 16 July 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Primary: 32A60: Zero sets of holomorphic functions 32L10: Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F05, 18F20, 55N30] 81Q50: Quantum chaos [See also 37Dxx]
Zelditch, Steve; Zhou, Peng. Central limit theorem for spectral partial Bergman kernels. Geom. Topol. 23 (2019), no. 4, 1961--2004. doi:10.2140/gt.2019.23.1961. https://projecteuclid.org/euclid.gt/1563242523