Consider the Aldous Markov chain on the space of rooted binary trees with n labeled leaves in which at each transition a uniform random leaf is deleted and reattached to a uniform random edge. Now, fix 1 ≤ k<n and project the leaf mass onto the subtree spanned by the first k leaves. This yields a binary tree with edge weights that we call a “decorated k‐tree with total mass n.” We introduce label swapping dynamics for the Aldous chain so that, when it runs in stationarity, the decorated k‐trees evolve as Markov chains themselves, and are projectively consistent over k. 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 the n→∞ continuum analog of the Aldous chain and will be taken up elsewhere.

中文翻译：

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Aldous链在二叉树上的投影：缠绕和一致性

考虑在带有n个标记叶子的生根二叉树的空间上的Aldous Markov链，其中在每个过渡处，均一的随机叶被删除并重新附加到均一的随机边缘。现在，修复1≤  ķ < Ñ并投影叶质量上的子树通过跨越所述第一ķ叶子。这产生了具有边缘权重的二叉树，我们称其为“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，当它平稳运行时，装饰的k树会随着马尔可夫链自身的变化而演化，并且在k上投射一致。投影一致链的构建是本文作者在连续树上构建Aldous扩散的关键步骤，这是Aldous链的n → ∞连续谱类似物，将在其他地方进行介绍。