高阶、极坐标和Sz.-单位圆上零点独立同分布的随机多项式的Nagy广义导数
Higher Order, Polar and Sz.-Nagy's Generalized Derivatives of Random Polynomials with Independent and Identically Distributed Zeros on the Unit Circle
摘要：
对于具有独立同分布的随机多项式，（独立同分布）零点服从任何公共概率分布$μ$，其支撑包含在单位圆内，证明了它们的一阶和高阶导数零点的经验测度弱收敛于$μ$ a. s.（几乎必然）。这，特别是，完成了最近的工作Subramanian的一阶导数的情况下，$μ$被假定为非均匀的。同样的a.s.弱收敛也将显示为极坐标和Sz。Nagy的广义导数，在一些较弱的条件下.
英文摘要：
For random polynomials with i.i.d. (independent and identically distribu-ted) zeros following any common probability distribution $μ$ with support contained in the unit circle, the empirical measures of the zeros of their first and higher order derivatives will be proved to converge weakly to $μ$ a.s. (almost sure(ly)). This, in particular, completes a recent work of Subramanian on the first order derivative case where $μ$ was assumed to be non-uniform. The same a.s. weak convergence will also be shown for polar and Sz.-Nagy's generalized derivatives, on some mild conditions.
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