We prove the asymptotic of the logarithmic Bergman kernel. And as an application, we calculate the conditional expectation of density of zeros of Gaussian random sections of powers of a positive line bundle that vanish along a fixed smooth subvariety.

中文翻译：

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对数Bergman核与高斯全纯场的条件期望

我们证明了对数Bergman核的渐近性。作为应用，我们计算了正线束的幂的高斯随机截面的零密度的条件期望值，该密度沿着固定的光滑子变量消失。