A non-local Random Walk on the Hypercube

Evita Nestoridi

A non-local Random Walk on the Hypercube

Probability 2017-09-21 v3 Combinatorics

Authors: Evita Nestoridi

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 $\frac{n}{2k}$ .

Keywords

random walks mixing times random walk in random environment

Cite

@article{arxiv.1507.05690,
  title  = {A non-local Random Walk on the Hypercube},
  author = {Evita Nestoridi},
  journal= {arXiv preprint arXiv:1507.05690},
  year   = {2017}
}

Comments

17 pages, accepted for publication by the Applied Probability Trust in Advances in Applied Probability 49.4 (December 2017)

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