Geodesic
Mixing time for a random walk on rooted trees
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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We define an analog of Plancherel measure for the set of rooted unlabeled trees on $n$ vertices, and a Markov chain which has this measure as its stationary distribution. Using the combinatorics of commutation relations, we show that order $n^2$ steps are necessary and suffice for convergence to the stationary distribution.
DOI : 10.37236/228
Classification : 05C81, 05C05, 60C05 
@article{10_37236_228,
     author = {Jason Fulman},
     title = {Mixing time for a random walk on rooted trees},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/228},
     zbl = {1206.05092},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/228/}
}
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Jason Fulman. Mixing time for a random walk on rooted trees. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/228

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