Durrett's mixing-time conjecture for lazy random walk on random 3-regular graphs

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Let G∼G(n,3)G\sim\mathcal{G}(n,3) be a random 33-regular graph, and consider the lazy random walk on GG. Its mixing time is measured in total variation and the lazy walk stays in place with probability 1/21/2 at each step. Durrett's conjecture. The mixing time for the lazy random walk on the random 33-regular graph is asymptotically

6log⁡2n.6\log_2 n.

Durrett's conjecture gives the conjectured sharp value of the asymptotic mixing time following the previously established lower bound; the source does not state whether it has been resolved.

References

Primary source

Eyal Lubetzky and Allan Sly, “Cutoff phenomena for random walks on random regular graphs”, arXiv:0812.0060 (2009).

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