Mixing Time for a Random Walk on Rooted Trees

Jason Fulman

Abstract


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.


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