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MR2135733 60J10 (60K35)
Benjamini, Itai; Berger, Noam; Hoffman, Christopher; Mossel, Elchanan Mixing times of the biased card shuffling and the asymmetric exclusion process. Trans. Amer. Math. Soc. 357 (2005), no. 8, 3013–3029.
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