Open Access
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 n32π2logn, 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

Keywords: adjacent transpositions , Cutoff phenomenon , Markov chains , mixing time , time inhomogeneous card shuffles

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.29 • No. 6 • December 2019
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