标题： 吉布斯碎片树 显示英文标题

标题： Gibbs fragmentation trees

摘要： 我们研究吉布斯型的分裂数。 在二元情况下，我们确定最一般的吉布斯型分裂数与奥利弗的beta分裂模型相一致，其参数范围相对于它所基于的$\beta>-2$ 概率分布有所扩展。${\rm Beta}(\beta+1,\beta+1)$ 在多分叉情况下，我们证明吉布斯碎片树与交换随机划分的两参数泊松-狄利克雷模型相关，其参数范围扩展为$\bN$，包括$0\le\alpha\le 1$，$\theta\ge -2\alpha$和$\alpha<0$，$\theta=-m\alpha$，$m\in\bN$。 显示英文摘要

摘要： We study fragmentation trees of Gibbs type. In the binary case, we identify the most general Gibbs type fragmentation tree with Aldous's beta-splitting model, which has an extended parameter range $\beta>-2$ with respect to the ${\rm Beta}(\beta+1,\beta+1)$ probability distributions on which it is based. In the multifurcating case, we show that Gibbs fragmentation trees are associated with the two-parameter Poisson-Dirichlet models for exchangeable random partitions of $\bN$, with an extended parameter range $0\le\alpha\le 1$, $\theta\ge -2\alpha$ and $\alpha<0$, $\theta=-m\alpha$, $m\in\bN$.