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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.29
URN: urn:nbn:de:0030-drops-75787
URL: http://drops.dagstuhl.de/opus/volltexte/2017/7578/
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Ben-Hamou, Anna ; Peres, Yuval

Cutoff for a Stratified Random Walk on the Hypercube

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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).

BibTeX - Entry

@InProceedings{benhamou_et_al:LIPIcs:2017:7578,
  author =	{Anna Ben-Hamou and Yuval Peres},
  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 =	{Klaus Jansen and Jos{\'e} D. P. Rolim and David Williamson and Santosh S. Vempala},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7578},
  URN =		{urn:nbn:de:0030-drops-75787},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.29},
  annote =	{Keywords: Mixing times, cutoff, hypercube}
}

Keywords: Mixing times, cutoff, hypercube
Seminar: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)
Issue Date: 2017
Date of publication: 31.07.2017


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