On sensitivity of uniform mixing times

Abstract

We show that the order of the $L_{\infty }$-mixing time of simple random walks on a sequence of uniformly bounded degree graphs of size $n$ may increase by an optimal factor of $\Theta (\log \log n)$ as a result of a bounded perturbation of the edge weights. This answers a question and a conjecture of Kozma.

15 pages. In this version various references were added and some typos were corrected

References in corpus (3)

• On sensitivity of mixing times and cutoff
• Mixing time bounds via bottleneck sequences
• On the precision of the spectral profile

Cited by in corpus (5)

• On sensitivity of mixing times and cutoff
• Mixing time bounds via bottleneck sequences
• Sensitivity of mixing times of Cayley graphs
• Cutoff for random walk on random graphs with a community structure
• Sensitivity of mixing times, an example