论文标题
概率极限定理由多项式的零引起
Probabilistic Limit Theorems Induced by the Zeros of Polynomials
论文作者
论文摘要
研究了离散随机变量的序列，其概率生成函数在正面真实轴周围的复杂平面的扇区中无零。陈述了所有订单的累积物上的急剧界限，导致浆果 - 埃森的边界，中等偏差结果，浓度不平等和mod-gaussisian收敛。另外，提供了一类多项式的累积量绑定的累积常数的替代证明。详细讨论了各种示例。
Sequences of discrete random variables are studied whose probability generating functions are zero-free in a sector of the complex plane around the positive real axis. Sharp bounds on the cumulants of all orders are stated, leading to Berry-Esseen bounds, moderate deviation results, concentration inequalities and mod-Gaussian convergence. In addition, an alternate proof of the cumulant bound with improved constants for a class of polynomials all of whose roots lie on the unit circle is provided. A variety of examples is discussed in detail.
