Cutoff for a stratified random walk on the hypercube

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).