Mixing of a random walk on a randomly twisted hypercube

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• Zsuzsa Baran (Cambridge)
• Tuesday 20 May 2025, 14:00-15:00
• MR12.

If you have a question about this talk, please contact Perla Sousi.

We consider `randomly twisted hypercubes’, i.e.\ random graphs $G^{$ for $n\ge0$ that can be defined recursively as follows. Let $G}{(0)}$ be a graph consisting of a single vertex, and for $n\ge1$ let $G^{$ be obtained by considering two independent copies $G}{(n-1,1)}$ and $G^{$ of $G}{(n-1)}$ and adding the edges corresponding to a uniform random matching between their vertices. We study a lazy or simple random walk on these and in both cases establish that their mixing times are of order $n$ and they do not exhibit cutoff. In this talk I hope to have enough time to discuss this model and the results and also present most of the ideas of the proofs. Joint work with An{\dj}ela \v{S}arkovi\’c; based on a joint work with Jonathan Hermon, An{\dj}ela \v{S}arkovi\’c, Allan Sly and Perla Sousi.

This talk is part of the Probability series.

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