Number variance of random zeros on complex manifolds

Details Number variance of random zeros on complex manifolds Number variance of random zeros on complex manifolds

2006-08-30

arxiv.org/abs/math/0608743v3

Geom. Funct. Anal. 18 (2008), 1422-1475.

Mathematics

Complex Variables

Some computations are simplified and positivity of the coefficient of the leading term in the variance formula is shown for al

Scientific paper

We show that the variance of the number of simultaneous zeros of $m$ i.i.d. Gaussian random polynomials of degree $N$ in an open set $U \subset C^m$ with smooth boundary is asymptotic to $N^{m-1/2} \nu_{mm} Vol(\partial U)$, where $\nu_{mm}$ is a universal constant depending only on the dimension $m$. We also give formulas for the variance of the volume of the set of simultaneous zeros in $U$ of $k

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