Open Access
2018 Cutoff for a stratified random walk on the hypercube
Anna Ben-Hamou, Yuval Peres
Electron. Commun. Probab. 23: 1-10 (2018). DOI: 10.1214/18-ECP132


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).


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Anna Ben-Hamou. Yuval Peres. "Cutoff for a stratified random walk on the hypercube." Electron. Commun. Probab. 23 1 - 10, 2018.


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

zbMATH: 1397.60096
MathSciNet: MR3812064
Digital Object Identifier: 10.1214/18-ECP132

Primary: 60J10

Keywords: Cutoff , hypercube , Markov chains , Mixing times

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