| Convergence of random zeros on complex manifolds |
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| 作者单位： | Department of |
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| 摘 要： | We show that the zeros of random sequences of Gaussian systems of polynomials of in- creasing 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,orthonor- malized on a regular compact set K(?)C~m,almost surely converge to the equilibrium measure on K as N→∞.
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| 收稿时间： | 17 August 2007 |
| 修稿时间： | 18 January 2008 |
Convergence of random zeros on complex manifolds |
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| Authors: | Bernard Shiffman |
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| Institution: | Bernard SHIFFMAN Department of Mathematics;Johns Hopkins University;Baltimore;MD 21218;USA |
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| 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 set K ⊂ ℂ
m
, almost surely converge to the equilibrium measure on K as N → ∞.
Research partially supported by the Notional Science Foundation (Grant No. DMS-0600982) |
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| Keywords: | random polynomial ample line bundle zeros of holomorphic sections equilibrium measure |
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