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Sensitivity of mixing times, an example

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arxiv 2105.05766 v1 pith:G3POGCPZ submitted 2021-05-12 math.PR

classification math.PR
keywords mixingtimearbitrarilyboundedconstructdegreeexamplefamily
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abstract

We construct a family of growing finite bounded degree rooted graphs, $G_n$, in which the mixing time for simple random walk, starting at the root, is order $\log |G_n|$. Yet after a quasi - isometry, the ratio of $|G_n|$ over the mixing time grows arbitrarily slow to infinity.

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