Cutoff for random to random card shuffle

Megan Bernstein, Evita Nestoridi

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)3303-3320
Number of pages18
JournalAnnals of Probability
Volume47
Issue number5
DOIs
StatePublished - 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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