Projections of the Aldous chain on binary trees: Intertwining and consistency
Projections of the Aldous chain on binary trees: Intertwining and consistency
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奥尔德斯链在二叉树上的投影：交织和一致性
DOI：
10.1002/rsa.20930
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发表时间：
2020
影响因子：
1
通讯作者：
Winkel, Matthias
中科院分区：
文献类型：
--
作者：
Forman, Noah;Pal, Soumik;Rizzolo, Douglas;Winkel, Matthias
考虑具有n个标记叶子的有根二叉树空间上的Aldous马尔可夫链，其中在每次转移中删除一个均匀随机叶子并重新连接到一个均匀随机边缘。现在，fix 1 ≤k<k将叶质量投影到第一个kleaves所跨越的子树上。这就产生了一个带有边权重的二叉树，我们称之为“总质量为n的装饰k树”。我们为Aldous链引入标签交换动力学，这样，当它在平稳性中运行时，装饰的k-树本身就像马尔可夫链一样进化，并且是投射一致的overk。投射相容链的构造是本文作者在连续树上构造Aldous扩散的关键步骤，它是Aldous链的→∞连续模拟，将在其他地方讨论。
Consider the Aldous Markov chain on the space of rooted binary trees withnlabeled leaves in which at each transition a uniform random leaf is deleted and reattached to a uniform random edge. Now, fix 1 ≤k<nand project the leaf mass onto the subtree spanned by the firstkleaves. This yields a binary tree with edge weights that we call a “decoratedk‐tree with total massn.” We introduce label swapping dynamics for the Aldous chain so that, when it runs in stationarity, the decoratedk‐trees evolve as Markov chains themselves, and are projectively consistent overk. The construction of projectively consistent chains is a crucial step in the construction of the Aldous diffusion on continuum trees by the present authors, which is then→∞continuum analog of the Aldous chain and will be taken up elsewhere.