Abstract
We study the cyclic adjacent transposition (CAT) shuffle of $n$ cards, which is a systematic scan version of the random adjacent transposition (AT) card shuffle. In this paper, we prove that the CAT shuffle exhibits cutoff at $\frac{n^{3}}{2\pi^{2}}\log n$, which concludes that it is twice as fast as the AT shuffle. This is the first verification of cutoff phenomenon for a time-inhomogeneous card shuffle.
Citation
Danny Nam. Evita Nestoridi. "Cutoff for the cyclic adjacent transposition shuffle." Ann. Appl. Probab. 29 (6) 3861 - 3892, December 2019. https://doi.org/10.1214/19-AAP1495
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