Sensitivity of mixing times, an example

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.

References in corpus (3)

• On sensitivity of uniform mixing times
• On sensitivity of mixing times and cutoff
• Sensitivity of mixing times of Cayley graphs