A Card Shuffling Analysis of Deformations of the Plancherel Measure of the Symmetric Group
نویسنده
چکیده
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.
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We study deformations of the Plancherel measure of the symmetric group by lifting them to the symmetric group and using combina-torics of card shuffling. The existing methods for analyzing deformations of Plancherel measure are not obviously applicable to the examples in this paper. The main idea of this paper is to find and analyze a formula for the total variation distance between iterations ...
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 11 شماره
صفحات -
تاریخ انتشار 2004