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摘要翻译：
给出了紧Kaehler流形上N次随机多项式的零集的区域U内体积的渐近大偏差估计，或者更一般地，正线丛的N次方全纯截面的区域U内体积的渐近大偏差估计。特别地，我们表明，对于所有$\delta>0$，该卷与其平均值相差超过$\deltaN$的概率小于$\exp(-c_{\delta，U}n^{m+1}）$，对于某个常数$c_{\delta，U}>0$.因此，随机截面在U中不消失的“空穴概率”有一个形式为$\exp(-c_{U}n^{m+1}）$的上界。
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英文标题：
《Overcrowding and hole probabilities for random zeros on complex
manifolds》
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作者：
Bernard Shiffman, Steve Zelditch, Scott Zrebiec
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Complex Variables 复变数
分类描述：Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves
全纯函数，自守群作用与形式，伪凸性，复几何，解析空间，解析束
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
We give asymptotic large deviations estimates for the volume inside a domain U of the zero set of a random polynomial of degree N, or more generally, of a holomorphic section of the N-th power of a positive line bundle on a compact Kaehler manifold. In particular, we show that for all $\delta>0$, the probability that this volume differs by more than $\delta N$ from its average value is less than $\exp(-C_{\delta,U}N^{m+1})$, for some constant $C_{\delta,U}>0$. As a consequence, the "hole probability" that a random section does not vanish in U has an upper bound of the form $\exp(-C_{U}N^{m+1})$.
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PDF链接：
https://arxiv.org/pdf/0805.2598
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