论文标题
随机零在复杂歧管上的差异扩展
Asymptotic expansion of the variance of random zeros on complex manifolds
论文作者
论文摘要
随机零集的线性统计量是零设置上平滑微分形式的积分，因此是固定域内随机零集的体积的平滑类似物。我们得出了一个渐近膨胀，以实现紧凑型kähler歧管上正线束的随机全态截面的零分隔线的方差。这种扩展使Shiffman-Zelditch在2010年给予的前阶渐近渐近造型（在Condimension One案例中）。
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.
