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Chen Shang

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Preprint Jul 2026

Hitting time mixing for random $k$-cycles

In this paper, we study the random walk on the symmetric group $\mathfrak{S}_n$ generated by the conjugacy class of $k$-cycles, where $2\le k=o(n/(\log n)^4)$. We prove that the walk exhibits hitting-time mixing: at the first time when every card has been touched, the distribution is already close to equilibrium. For o...

Chen Shang, Jiahe Shen, Jiyue Zeng et al. · 1 citation

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