Cutoff for the cyclic adjacent transposition shuffle

Danny Nam; Evita Nestoridi

doi:10.1214/19-AAP1495

Cutoff for the cyclic adjacent transposition shuffle

Danny Nam, Evita Nestoridi

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 ₂ ⁿ _π ³ ₂ logn, 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.

Original language	English (US)
Pages (from-to)	3861-3892
Number of pages	32
Journal	Annals of Applied Probability
Volume	29
Issue number	6
DOIs	https://doi.org/10.1214/19-AAP1495
State	Published - 2019

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Adjacent transpositions
Cutoff phenomenon
Markov chains
Mixing time
Time inhomogeneous card shuffles
We are grateful to Yuval Peres and Allan Sly for their helpful comments

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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 2 n π 3 2 logn, 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.",

keywords = "Adjacent transpositions, Cutoff phenomenon, Markov chains, Mixing time, Time inhomogeneous card shuffles, We are grateful to Yuval Peres and Allan Sly for their helpful comments",

author = "Danny Nam and Evita Nestoridi",

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AU - Nestoridi, Evita

N1 - Publisher Copyright: © Institute of Mathematical Statistics, 2019

PY - 2019

Y1 - 2019

N2 - 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 2 n π 3 2 logn, 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.

AB - 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 2 n π 3 2 logn, 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.

KW - Adjacent transpositions

KW - Cutoff phenomenon

KW - Markov chains

KW - Mixing time

KW - Time inhomogeneous card shuffles

KW - We are grateful to Yuval Peres and Allan Sly for their helpful comments

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JF - Annals of Applied Probability

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Cutoff for the cyclic adjacent transposition shuffle

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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