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September 2019 Cutoff for random to random card shuffle
Megan Bernstein, Evita Nestoridi
Ann. Probab. 47(5): 3303-3320 (September 2019). DOI: 10.1214/19-AOP1340

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 $\frac{3}{4}n\log n-\frac{1}{4}n\log\log{n}$ with window of order $n$, answering a conjecture of Diaconis.

Citation

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Megan Bernstein. Evita Nestoridi. "Cutoff for random to random card shuffle." Ann. Probab. 47 (5) 3303 - 3320, September 2019. https://doi.org/10.1214/19-AOP1340

Information

Received: 1 March 2017; Revised: 1 January 2019; Published: September 2019
First available in Project Euclid: 22 October 2019

zbMATH: 07145318
MathSciNet: MR4021252
Digital Object Identifier: 10.1214/19-AOP1340

Subjects:
Primary: 05E99, 20C30, 60J10

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 5 • September 2019
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