Cutoff for a stratified random walk on the hypercube

Anna Ben-Hamou, Yuval Peres

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 $3/2 nlogn$ with window of size $n$, solving a question posed by Chung and Graham (1997).