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arXiv · 1705.06153

Cutoff for a stratified random walk on the hypercube

Anna Ben-Hamou·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).

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Anna Ben-Hamou, Yuval Peres. 2017-05-17. Cutoff for a stratified random walk on the hypercube. https://arxiv.org/abs/1705.06153

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