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Analysis of a non-reversible Markov chain speedup by a single edge
Balázs Gerencsér · 2019-05-09 · via math.PR updates on arXiv.org

We present a Markov chain example where non-reversibility and an added edge jointly improve mixing time: when a random edge is added to a cycle of $n$ vertices and a Markov chain with a drift is introduced, we get mixing time of $O(n^{3/2})$ with probability bounded away from 0. If only one of the two modifications were performed, the mixing time would stay $Ω(n^2)$.

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