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Cutoff for a Stratified Random Walk on the Hypercube

Authors: Anna Ben-Hamou and Yuval Peres

Published in: LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)


Abstract
We consider the random walk on the hypercube which moves by picking an ordered pair (i,j) of distinct coordinates uniformly at random and adding the bit at location i to the bit at location j, modulo 2. We show that this Markov chain has cutoff at time (3/2)n*log(n) with window of size n, solving a question posed by Chung and Graham (1997).

Cite as

Anna Ben-Hamou and Yuval Peres. Cutoff for a Stratified Random Walk on the Hypercube. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 29:1-29:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{benhamou_et_al:LIPIcs.APPROX-RANDOM.2017.29,
  author =	{Ben-Hamou, Anna and Peres, Yuval},
  title =	{{Cutoff for a Stratified Random Walk on the Hypercube}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{29:1--29:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.29},
  URN =		{urn:nbn:de:0030-drops-75787},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.29},
  annote =	{Keywords: Mixing times, cutoff, hypercube}
}
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