Central limit theorem for spectral partial bergman kernels

Steve Zelditch, Peng Zhou

Research output: Contribution to journalArticlepeer-review


Partial Bergman kernels Πk,Eare kernels of orthogonal projections onto subspaces Sk⊂ H0(M,Lk) of holomorphic sections of the kth power of an ample line bundle over a Kähler manifold (M; Ω). The subspaces of this article are spectral subspaces f Hk≤ Eg of the Toeplitz quantization Hkof a smooth Hamiltonian H : M → R. It is shown that the relative partial density of states Πk,E(z)/Πk(z)→ 1A where A = fH < Eg. Moreover it is shown that this partial density of states exhibits 'Erf'-asymptotics along the interface ∂A, that is, the density profile asymptotically has a Gaussian error function shape interpolating between the values 1; 0 of 1A. Such 'erf'-asymptotics are a universal edge effect. The different types of scaling asymptotics are reminiscent of the law of large numbers and central limit theorem.

Original languageEnglish (US)
JournalUnknown Journal
StatePublished - Aug 30 2017

ASJC Scopus subject areas

  • General

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