The Rook's Walk on an n^d chessboard exhibits cutoff at mixing time (d n log n)/2 with explicit constants obtained from the eigenvalues of its lumped birth-death projection.
Generating a random permutation with random transpositions
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Mixing Times and Cutoff for the Rook's Walk
The Rook's Walk on an n^d chessboard exhibits cutoff at mixing time (d n log n)/2 with explicit constants obtained from the eigenvalues of its lumped birth-death projection.