LIPIcs.APPROX-RANDOM.2017.29.pdf
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Cutoff for a Stratified Random Walk on the Hypercube
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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Randomization and Computation (RANDOM)
Conference: International Conference on Approximation Algorithms for Combinatorial Optimization Problems (APPROX) - License:
Creative Commons Attribution 3.0 Unported license
- Publication date: 2017-08-11
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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)
https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2017.29
https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2017.29
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).
Keywords
- Mixing times
- cutoff
- hypercube
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