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arXiv · 2112.05085

Mixing times of one-sided $k$-transposition shuffles

Evita Nestoridi·Kenny Peng·Bryan Wong
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Abstract

We study mixing times of the one-sided $k$-transposition shuffle. We prove that this shuffle mixes relatively slowly, even for $k$ big. Using the recent ``lifting eigenvectors'' technique of Dieker and Saliola and applying the $\ell^2$ bound, we prove different mixing behaviors and explore the occurrence of cutoff depending on $k$.

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Evita Nestoridi, Kenny Peng, Bryan Wong. 2021-12-09. Mixing times of one-sided $k$-transposition shuffles. https://arxiv.org/abs/2112.05085

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