论文标题
一条在多叶树上持续标签的沿链链
A down-up chain with persistent labels on multifurcating trees
论文作者
论文摘要
在本文中，我们建议研究一个向上的马尔可夫链的一般概念，用于用n个标记的叶子的多发性树木。我们详细研究了与Chen等人的$（α，γ）$ - 模型相关的链条。 （2009年），概括并进一步发展了Forman等人的先前工作。 （2018，2020）在二进制特殊情况下。我们部署的技术利用了具有平面结构的树木上的增长过程的构建和向上的马尔可夫链。我们的施工确保了向上链的自然预测本身就是马尔可夫连锁店。我们建立了标签动力学，同时保留标记的α-伽马分布，并在所有k的最大标签上保持最小标签的分支点，以$ n^2 $时间步长。我们猜想存在扩散缩放限制，从而限制了Forman等人的“ Aldous扩散”的概括。 （2018+）作为连续树值的过程和Löhr等人的“代数α福音树的演化”。 （2018+）以及Nussbaumer和Winter（2020）作为代数树空间中的一个过程。
In this paper, we propose to study a general notion of a down-up Markov chain for multifurcating trees with n labelled leaves. We study in detail down-up chains associated with the $(α, γ)$-model of Chen et al. (2009), generalising and further developing previous work by Forman et al. (2018, 2020) in the binary special cases. The technique we deploy utilizes the construction of a growth process and a down-up Markov chain on trees with planar structure. Our construction ensures that natural projections of the down-up chain are Markov chains in their own right. We establish label dynamics that at the same time preserve the labelled alpha-gamma distribution and keep the branch points between the k smallest labels for order $n^2$ time steps for all k larger than 2. We conjecture the existence of diffusive scaling limits generalising the "Aldous diffusion" by Forman et al. (2018+) as a continuum-tree-valued process and the "algebraic α-Ford tree evolution" by Löhr et al. (2018+) and by Nussbaumer and Winter (2020) as a process in a space of algebraic trees.
