标题： Gibbs碎片化树 显示英文标题

标题： Gibbs fragmentation trees

摘要： 我们研究了Gibbs类型的碎裂树。在二元情况下，我们确定了最广义的Gibbs类型碎裂树与Aldous的beta-分裂模型一致，该模型相对于基于其上的$\beta>-2$概率分布具有扩展的参数范围${\rm beta}(\beta+1,\beta+1)$。 在多分支的情况下，我们证明了Gibbs碎片化树与用于交换随机划分的双参数Poisson-Dirichlet模型有关，这些模型适用于 $\mathbb {N}$的交换随机划分，扩展的参数范围包括 $0\le\alpha\le1$, $\theta\ge-2\alpha$和 $\alpha<0$, $\theta =-m\alpha$, $m\in \mathbb {N}$。 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' 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 $\mathbb {N}$, with an extended parameter range $0\le\alpha\le1$, $\theta\ge-2\alpha$ and $\alpha<0$, $\theta =-m\alpha$, $m\in \mathbb {N}$.