Electronic Communications in Probability

Cutoff for a stratified random walk on the hypercube

Anna Ben-Hamou and Yuval Peres

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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 $\frac{3} {2}n\log n$ with window of size $n$, solving a question posed by Chung and Graham (1997).

Article information

Source
Electron. Commun. Probab., Volume 23 (2018), paper no. 32, 10 pp.

Dates
Received: 12 December 2017
Accepted: 10 April 2018
First available in Project Euclid: 26 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1527300061

Digital Object Identifier
doi:10.1214/18-ECP132

Mathematical Reviews number (MathSciNet)
MR3812064

Zentralblatt MATH identifier
1397.60096

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
Markov chains mixing times cutoff hypercube

Rights
Creative Commons Attribution 4.0 International License.

Citation

Ben-Hamou, Anna; Peres, Yuval. Cutoff for a stratified random walk on the hypercube. Electron. Commun. Probab. 23 (2018), paper no. 32, 10 pp. doi:10.1214/18-ECP132. https://projecteuclid.org/euclid.ecp/1527300061


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References

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