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arXiv 1312.0933math.CVmath.AGmath.PR
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随机全纯截面零点的等分布

Equidistribution of zeros of random holomorphic sections

Syracuse University(雪城大学)

Turgay Bayraktar

AI总结:

研究随机全纯截面在高次正线丛上零点的渐近分布,证明了在正则紧致集上正交多项式线性组合的归一化零测度几乎必然趋于该集的均衡测度。

摘要:

我们研究随机全纯截面在高次正线丛上零点的渐近分布。我们考虑了一类广泛的分布,包括实数和复数高斯分布。作为特殊情况,我们得到多元复多项式在由正交多项式线性组合且具有独立同分布随机系数时的渐近零分布。具体而言,我们证明了在正则紧致集$K\subset \Bbb{C}^m$上正交化的m个独立同分布随机多项式的归一化零测度几乎必然趋于K的均衡测度。

英文摘要:

We study asymptotic distribution of zeros of random holomorphic sections of high powers of positive line bundles defined over projective homogenous manifolds. We work with a wide class of distributions that includes real and complex Gaussians. As a special case, we obtain asymptotic zero distribution of multivariate complex polynomials given by linear combinations of orthogonal polynomials with i.i.d. random coefficients. Namely, we prove that normalized zero measures of m i.i.d random polynomials, orthonormalized on a regular compact set $K\subset \Bbb{C}^m,$ are almost surely asymptotic to the equilibrium measure of $K$.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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