论文标题
间隔分区空间的扩散：两参数模型
Diffusions on a space of interval partitions: The two-parameter model
论文作者
论文摘要
我们使用Poisson--二硫酸属$（α，θ）$ sentary分布的参数$α\ in（0,1）$和$θ\ ge 0 $介绍和研究间隔分区扩散。这扩展了对$（α，0）$和$（α，α）$的以前的工作，并基于我们最近在测量值扩散的工作。我们处理一般$θ\ ge 0 $的方法使我们能够在特殊情况下加强以前的工作，包括带有灰尘的初始间隔分区。与衡量标准的设置相反，我们可以证明这一扩展过程是对该环境中建立的狩猎财产的改进的磨难过程。这些过程可以看作是整数组成的分支图的边界上的扩散。实际上，通过在合适的准对称函数上研究其无限发电机，我们将它们与作为缩放限制的上链链的缩放限制获得的扩散联系起来。
We introduce and study interval partition diffusions with Poisson--Dirichlet$(α,θ)$ stationary distribution for parameters $α\in(0,1)$ and $θ\ge 0$. This extends previous work on the cases $(α,0)$ and $(α,α)$ and builds on our recent work on measure-valued diffusions. Our methods for dealing with general $θ\ge 0$ allow us to strengthen previous work on the special cases to include initial interval partitions with dust. In contrast to the measure-valued setting, we can show that this extended process is a Feller process improving on the Hunt property established in that setting. These processes can be viewed as diffusions on the boundary of a branching graph of integer compositions. Indeed, by studying their infinitesimal generator on suitable quasi-symmetric functions, we relate them to diffusions obtained as scaling limits of composition-valued up-down chains.
