Mixing time under monotone censoring

Yiming Chen; Yuval Peres

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arXiv · 2609.16515

Mixing time under monotone censoring

Yiming Chen·Yuval Peres

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Abstract

We prove that the lazy random walk on the discrete cube, censored to any increasing set of fixed positive density, mixes in time $O(n\log n)$, answering a question of Ding and Mossel. More precisely, for every nonempty increasing set $A\subseteq \{0,1\}^n$, \begin{equation} t_{\mathrm{mix}}(P) \le Kμ(A)^{-3}n\log(en). \label{eq:mixing-time-bound} \end{equation} where $μ$ is uniform on the cube and $K$ is an absolute constant. The proof uses hypercontractivity on the ambient cube to strengthen Poincaré inequality on coordinate sections. A stopping-time occupation inequality for increasing sets converts the resulting local bound into a uniform bound on hitting times of large sets. See the appendix for a better estimates of the constant and the dependence on $μ(A)$.

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Yiming Chen, Yuval Peres. 2026-09-15. Mixing time under monotone censoring. https://arxiv.org/abs/2609.16515

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