论文标题
mod- $ $φ$ contergence of stirl分布的收敛，并限制其生成功能的零的定理
Mod-$φ$ convergence of Stirling distributions and limit theorems for zeros of their generating functions
论文作者
论文摘要
我们研究了几个概率分布在涉及两种stirling数字的正整数上的几个概率分布的融合，并因此得出了这些分布的各种限制定理。我们还得出了与相应生成函数的零分布的密切相关定理。例如，当$ n $ balls在$θ$用$θ$与$ n $线性增长时，在$ n $ box中分配了$ n $ balls在$θ$ box中分配$ n $ balls时，我们确定了占用盒数量的多项式的零分布。
We study mod-$φ$ convergence of several probability distributions on the set of positive integers that involve Stirling numbers of both kinds and, as a consequence, derive various limit theorems for these distributions. We also derive closely related limit theorems for the distribution of zeros of the corresponding generating functions. For example, we identify the asymptotic distribution of zeros for the generating polynomial of the number of occupied boxes when $n$ balls are allocated equiprobably and independently among $θ$ boxes in the regime when $θ$ grows linearly with $n$.
