论文标题
Beta $（2-α，α）$的长度的联合波动 - 合并
The joint fluctuations of the lengths of the Beta$(2-α, α)$-coalescents
论文作者
论文摘要
我们认为beta $（2-α，α）$ - 与参数范围$ 1 <α<2 $的合并，从$ n $叶子开始。 $ n $ -beta $（2-α，α）$的订单$ r $的长度$ \ ell^{（n）} _ r $ $ r $ - 定义为携带带有$ r $叶子的子树的所有分支的长度的总和。我们表明，对于任何$ s \ in \ mathbb n $，适当集中和重新续订的订单长度的向量$ 1 \ le r \ le \ le \ le \ le s $分配给多变量稳定分布，因为叶子的数量倾向于无限。
We consider Beta$(2-α, α)$-coalescents with parameter range $1 <α<2$ starting from $n$ leaves. The length $\ell^{(n)}_r$ of order $r$ in the $n$-Beta$(2-α, α)$-coalescent tree is defined as the sum of the lengths of all branches that carry a subtree with $r$ leaves. We show that for any $s \in \mathbb N$ the vector of suitably centered and rescaled lengths of orders $1\le r \le s$ converges in distribution to a multivariate stable distribution as the number of leaves tends to infinity.
