Convergence of random zeros on complex manifolds

2007/08/21 by Bernard Shiffman · 1 citation
Mathematics · #math.CV #math.AG #math.PR

paper · pdf · doi:10.1007/s11425-008-0060-9

published as Sci. China Ser. A (Special issue for Qikeng Lu) 51 (2008), 707-720 · 16 pages

arxiv created 2007/08/21 · arxiv updated 2015/05/12

Abstract

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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• Tian's theorem for Grassmannian embeddings and degeneracy sets of random sections

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