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December 2019 Cutoff for the cyclic adjacent transposition shuffle
Danny Nam, Evita Nestoridi
Ann. Appl. Probab. 29(6): 3861-3892 (December 2019). DOI: 10.1214/19-AAP1495

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

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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

Information

Received: 1 September 2018; Revised: 1 April 2019; Published: December 2019
First available in Project Euclid: 7 January 2020

zbMATH: 07172348
MathSciNet: MR4047994
Digital Object Identifier: 10.1214/19-AAP1495

Subjects:
Primary: 60J10
Secondary: 60C05, 60G42

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 6 • December 2019
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