TY - JOUR

T1 - Central limit theorem for spectral partial bergman kernels

AU - Zelditch, Steve

AU - Zhou, Peng

N1 - Publisher Copyright:
Copyright © 2017, The Authors. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2017/8/30

Y1 - 2017/8/30

N2 - 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.

AB - 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.

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M3 - Article

AN - SCOPUS:85093371629

JO - Free Radical Biology and Medicine

JF - Free Radical Biology and Medicine

SN - 0891-5849

ER -