复流形上随机零点方差的渐近展开
Asymptotic expansion of the variance of random zeros on complex manifolds
摘要：
随机零集的线性统计是零集上的光滑微分形式的积分，因此是固定域内随机零集体积的光滑模拟。得到了紧致Kähler流形上正线丛的幂的随机全纯截面的零因子的线性统计量方差的渐近展开.这种扩展锐化了Shiffman-Zelditch在2010年给出的首阶渐近（在余维一种情况下）。
英文摘要：
Linear statistics of random zero sets are integrals of smooth differential forms over the zero set and as such are smooth analogues of the volume of the random zero set inside a fixed domain. We derive an asymptotic expansion for the variance of linear statistics of the zero divisors of random holomorphic sections of powers of a positive line bundle on a compact Kähler manifold. This expansion sharpens the leading-order asymptotics (in the codimension one case) given by Shiffman--Zelditch in 2010.
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