Convergence of random zeros on complex manifolds

Details Convergence of random zeros on complex manifolds Convergence of random zeros on complex manifolds

2007-08-21

arxiv.org/abs/0708.2754v1

Sci. China Ser. A (Special issue for Qikeng Lu) 51 (2008), 707-720

Mathematics

Complex Variables

16 pages

Scientific paper

We show that the zeros of random sequences of Gaussian systems of polynomials of increasing degree almost surely converge to the expected limit distribution under very general hypotheses. In particular, the normalized distribution of zeros of systems of m polynomials of degree N, orthonormalized on a regular compact subset K of C^m, almost surely converge to the equilibrium measure on K as the degree N goes to infinity.

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