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The Aldous chain on cladograms mixes in order $n^2$ steps
Cladograms of size $n$ are unrooted binary trees whose leaves are labelled from 1 to $n$. Aldous introduced in 2000 a Markov chain on cladograms, a step of which consists of removing a leaf uniformly at random and reinserting it on a uniformly chosen edge. We introduce a coupling for this walk, whic
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