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arXiv · 1507.05690

A non-local Random Walk on the Hypercube

Evita Nestoridi
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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} $.

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Evita Nestoridi. 2015-07-21. A non-local Random Walk on the Hypercube. https://arxiv.org/abs/1507.05690

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