Number variance of random zeros on complex manifolds, II: smooth statistics

Details Number variance of random zeros on complex manifolds, II: smooth statistics Number variance of random zeros on complex manifolds, II: smooth statistics

2007-11-12

arxiv.org/abs/0711.1840v1

Special issue in honor of Joseph J. Kohn, Pure Appl. Math. Q. 6 (2010), 1145-1167

Mathematics

Complex Variables

17 pages. This paper is a follow-up to arXiv:math/0608743v2 and includes the smooth statistics in the earlier version arXiv:ma

Scientific paper

We consider the zero sets $Z_N$ of systems of $m$ random polynomials of degree $N$ in $m$ complex variables, and we give asymptotic formulas for the random variables given by summing a smooth test function over $Z_N$. Our asymptotic formulas show that the variances for these smooth statistics have the growth $N^{m-2}$. We also prove analogues for the integrals of smooth test forms over the subvarieties defined by $k

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