Abstract
In this paper, we use the eigenvalues of the random to random card shuffle to prove a sharp upper bound for the total variation mixing time. Combined with the lower bound due to Subag, we prove that this walk exhibits cutoff at $\frac{3}{4}n\log n-\frac{1}{4}n\log\log{n}$ with window of order $n$, answering a conjecture of Diaconis.
Citation
Megan Bernstein. Evita Nestoridi. "Cutoff for random to random card shuffle." Ann. Probab. 47 (5) 3303 - 3320, September 2019. https://doi.org/10.1214/19-AOP1340
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