Number Variance of Random Zeros on Complex Manifolds
نویسنده
چکیده
We show that the variance of the number of simultaneous zeros ofm i.i.d. Gaussian random polynomials of degree N in an open set U ⊂ C with smooth boundary is asymptotic to N νmm Vol(∂U), where νmm 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 < m random degree-N polynomials on C. Our results hold more generally for the simultaneous zeros of random holomorphic sections of the N -th power of any positive line bundle over any m-dimensional compact Kähler manifold.
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