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    Improved bounds for the mixing time of the random-to-random insertion shuffle

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    We prove an upper bound of 1.5324nlogn1.5324 n \log n for the mixing time of the random-to-random insertion shuffle, improving on the best known upper bound of 2nlogn2 n \log n. Our proof is based on the analysis of a non-Markovian coupling.Comment: 7 pages, 1 figur
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