论文标题
上订购的中国餐厅流程具有双向移民，移民和扩散极限
Up-down ordered Chinese restaurant processes with two-sided immigration, emigration and diffusion limits
论文作者
论文摘要
我们介绍了一个三参数订购的中餐餐厅流程的三参数家族$ {\ rm pcrp}^{（α）}（θ_1，θ_2）$，$α\ in（0,1）$，$θ_1，$θ_1，θ_2，θ_2，θ_2\ ge 0 $，一般性的两位 - 居住家族的Rogers and Winkel。我们的主要结果建立了自相似的扩散极限，$ {\ rm ssip}^{（α）}（θ_1，θ_2）$ - 概括了间隔分区演变的现有家庭。我们使用缩放限制方法将平稳性结果扩展到整个三参数家族，并确定了一个大型泊松家庭 - 二里中的间隔分区。它们的间隔长度的排名序列具有Poisson-二硫次分布，带有参数$α\ in（0,1）$和$θ：=θ_1+θ_2-α\ ge-ge-α$，包括第一次使用$θ>-α$的范围，而不是限制为$θ\ ge ge ge 0 $。这在弗莱明（Fleming）中有应用 - viot过程，嵌套的间隔分区的演变和树值的马尔可夫过程，特别是依赖于扩展的参数范围。
We introduce a three-parameter family of up-down ordered Chinese restaurant processes ${\rm PCRP}^{(α)}(θ_1,θ_2)$, $α\in(0,1)$, $θ_1,θ_2\ge 0$, generalising the two-parameter family of Rogers and Winkel. Our main result establishes self-similar diffusion limits, ${\rm SSIP}^{(α)}(θ_1,θ_2)$-evolutions generalising existing families of interval partition evolutions. We use the scaling limit approach to extend stationarity results to the full three-parameter family, identifying an extended family of Poisson--Dirichlet interval partitions. Their ranked sequence of interval lengths has Poisson--Dirichlet distribution with parameters $α\in(0,1)$ and $θ:=θ_1+θ_2-α\ge-α$, including for the first time the usual range of $θ>-α$ rather than being restricted to $θ\ge 0$. This has applications to Fleming--Viot processes, nested interval partition evolutions and tree-valued Markov processes, notably relying on the extended parameter range.
