Schur--Weyl duality for diagonalizing a Markov chain on the hypercube

Abstract

We show how the tools of modern algebraic combinatorics -- representation theory, Murphy elements, and particularly Schur--Weyl duality -- can be used to give an explicit orthonormal basis of eigenfunctions for a "curiously slowly mixing Markov chain" on the space of binary $n$-tuples. The basis is used to give sharp rates of convergence to stationarity.

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