Year: 2026
Type: preprint
Abstract: 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, which follows multiple colored subtrees in parallel. We go around the lack of independence of the colored components by finding a relevant statistic, namely the sum of the squares of the sizes of all colored components, which we prove has a drift. We deduce that the mixing time of the walk is of order $n^2$, solving a conjecture of Aldous.
Source: arXiv (Cornell University)
Authors: Féray, Valentin, Teyssier, Lucas
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W7213429676