Cutoff for random to random card shuffle

Megan Bernstein; Evita Nestoridi

doi:10.1214/19-AOP1340

Cutoff for random to random card shuffle

Megan Bernstein
, Evita Nestoridi

Mathematics

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

12 Scopus citations

Abstract

In this paper, we use the eigenvalues of the random to random card shuffle to prove a sharp upper bound for the total variation mixing time. Combined with the lower bound due to Subag, we prove that this walk exhibits cutoff at 3/4 n log n-1/4 n log log n with window of order n, answering a conjecture of Diaconis.

Original language	English (US)
Pages (from-to)	3303-3320
Number of pages	18
Journal	Annals of Probability
Volume	47
Issue number	5
DOIs	https://doi.org/10.1214/19-AOP1340
State	Published - Sep 1 2019

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Card shuffle
Cutoff
Cyclic-to-random
Mixing times
Random-to-random

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10.1214/19-AOP1340

Cite this

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title = "Cutoff for random to random card shuffle",

abstract = "In this paper, we use the eigenvalues of the random to random card shuffle to prove a sharp upper bound for the total variation mixing time. Combined with the lower bound due to Subag, we prove that this walk exhibits cutoff at 3/4 n log n-1/4 n log log n with window of order n, answering a conjecture of Diaconis.",

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AU - Bernstein, Megan

AU - Nestoridi, Evita

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

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Y1 - 2019/9/1

N2 - In this paper, we use the eigenvalues of the random to random card shuffle to prove a sharp upper bound for the total variation mixing time. Combined with the lower bound due to Subag, we prove that this walk exhibits cutoff at 3/4 n log n-1/4 n log log n with window of order n, answering a conjecture of Diaconis.

AB - In this paper, we use the eigenvalues of the random to random card shuffle to prove a sharp upper bound for the total variation mixing time. Combined with the lower bound due to Subag, we prove that this walk exhibits cutoff at 3/4 n log n-1/4 n log log n with window of order n, answering a conjecture of Diaconis.

KW - Card shuffle

KW - Cutoff

KW - Cyclic-to-random

KW - Mixing times

KW - Random-to-random

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M3 - Article

AN - SCOPUS:85076760002

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EP - 3320

JO - Annals of Probability

JF - Annals of Probability

IS - 5

ER -

Cutoff for random to random card shuffle

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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