Equidistribution of zeros of random holomorphic sections
Equidistribution of zeros of random holomorphic sections
复制标题
随机全纯截面零点的均匀分布
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发表时间：
2013
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通讯作者：
Turgay Bayraktar
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作者：
Turgay Bayraktar
研究了射影齐性流形上正线性丛的高次幂的随机全纯截面零点的渐近分布。我们的工作与广泛的一类分布，包括真实的和复杂的高斯分布。作为特例，我们得到了由独立同分布的正交多项式的线性组合所给出的多元复多项式的渐近零分布。随机系数也就是说，我们证明了m i d随机多项式的归一化零测度，在正则紧集$K子集Bbb{C}^m，$上正交归一化，几乎必然渐近于$K$的平衡测度。
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 $Ksubset Bbb{C}^m,$ are almost surely asymptotic to the equilibrium measure of $K$.