Kostlan Shub Smale随机多项式系统实根个数的中心极限定理
Central Limit Theorem for the number of real roots of Kostlan Shub Smale random polynomial systems
摘要：
本文得到了任意大小的平方Kostlan-Shub-Smale随机多项式系统的实根的正规化个数的一个中心极限定理.需要研究根数的渐近方差，这个结果在[2]中得到。然后我们将根的个数表示为一个显式的非线性泛函，它属于It{}-Wiener混沌。这种表示法为应用四阶矩定理和此后的渐近正态性提供了一种工具。MSC 2010受试者分类：初级60 F05、30 C15;次级60 G60、65 H10。
英文摘要：
We obtain a Central Limit Theorem for the normalized number of real roots of a square Kostlan-Shub-Smale random polynomial system of any size as the degree goes to infinity. A study of the asymptotic variance of the number of roots is needed, this result was obtained in [2]. Afterwards we represent the number of roots as an explicit non linear functional belonging to the It{ô}-Wiener chaos. This representation provides a tool for applying the Fourth Moment Theorem and henceforth the asymptotic normality. MSC 2010 subject classifications: Primary 60F05, 30C15, ; secondary 60G60, 65H10.
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