Note: Random-to-front shuffles on trees

Abstract

A Markov chain is considered whose states are orderings of an underlying fixed tree and whose transitions are local "random-to-front" reorderings, driven by a probability distribution on subsets of the leaves. The eigenvalues of the transition matrix are determined using Brown's theory of random walk on semigroups.Comment: 6 pages, 4 figures; to appear in Electronic Communications in Probabilit