Geodesic
A card shuffling analysis of deformations of the Plancherel measure of the symmetric group
The electronic journal of combinatorics, Tome 11 (2004) no. 1
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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.
DOI : 10.37236/1774
Classification : 05A05, 60J10
Mots-clés : Plancherel measure, shuffles, permutation statistics, convergence rate 
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     author = {Jason Fulman},
     title = {A card shuffling analysis of deformations of the {Plancherel} measure of the symmetric group},
     journal = {The electronic journal of combinatorics},
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     number = {1},
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Jason Fulman. A card shuffling analysis of deformations of the Plancherel measure of the symmetric group. The electronic journal of combinatorics, Tome 11 (2004) no. 1. doi: 10.37236/1774

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