论文标题
关于复合泊松分布的高矩的渐近特性
On asymptotic properties of high moments of compound Poisson distribution
论文作者
论文摘要
我们研究矩$ m_k（λ）$ $ x_1+\ dots+x_ {n_λ} $的渐近行为，其中$n_λ$遵循poisson概率分布，其均值$λ$ and $ \ \ \ {x_j \} $是I.I.D.的家族。随机变量也独立于$n_λ$。我们获得了$ m_k（λ）$的明确表达式为$ k \ to \ infty $，并根据$λ=λ_k$的渐近行为进行研究。 在应用中，我们建立了大加权随机图的最大顶点度的浓度特性。另一个应用与大型随机矩阵矩的研究中产生的变量有关。最后，对于$ x_j $的三种特定概率分布的情况，我们对某些组合多项式的渐近行为进行评论，包括偶数分区的铃铛多项式。
We study asymptotic behavior of the moments $M_k(λ)$ of the sum $X_1+\dots+X_{N_λ}$, where $N_λ$ follows the Poisson probability distribution with mean value $λ$ and $\{X_j\}$ is a family of i.i.d. random variables also independent from $N_λ$. We obtain an explicit expression for the leading term of $M_k(λ)$ as $k\to\infty$ and study it in dependence of the asymptotic behavior of $λ= λ_k$. In application, we establish a concentration property of maximal vertex degree of large weighted random graphs. Another application is related with a variable that arises in the studies of high moments of large random matrices. Finally, regarding three particular cases of probability distribution of $X_j$, we comment on the asymptotic behavior of certain combinatorial polynomials, including the Bell polynomials of even partitions.
