A card shuffling analysis of deformations of the Plancherel measure of the symmetric group (Q1883631)

Summary: This paper finds and analyzes a formula for the total variation distance between iterations of riffle shuffles and iterations of ``cut and then riffle shuffle''. This allows one to obtain information about the convergence rate of permutation statistics (such as the length of the longest increasing subsequence or position of a given card) under these processes. Similar results are given for affine shuffles, which allow us to determine their convergence rate to randomness.