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A non-local Random Walk on the Hypercube (1507.05690v3)
Published 21 Jul 2015 in math.PR and math.CO
Abstract: This paper studies the random walk on the hypercube $(\mathbb{Z}/2\mathbb{Z})n$ which at each step flips $k$ randomly chosen coordinates. We prove that the mixing time for this walk is of order $\frac{n}{k} \log n$. We also prove that if $k=o(n)$, then the walk exhibits cutoff at $\frac{n}{2k} \log n$ with window $\frac{n}{2k} $.