{"ID":2894263,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.11031","arxiv_id":"2507.11031","title":"Rapid Mixing of Glauber Dynamics for Monotone Systems via Entropic Independence","abstract":"We study the mixing time of Glauber dynamics on monotone systems. For monotone systems satisfying the entropic independence condition, we prove a new mixing time comparison result for Glauber dynamics. For concrete applications, we obtain $\\tilde{O}(n)$ mixing time for the random cluster model induced by the ferromagnetic Ising model with consistently biased external fields, and $\\tilde{O}(n^2)$ mixing time for the bipartite hardcore model under the one-sided uniqueness condition, where $n$ is the number of variables in corresponding models, improving the best known results in [Chen and Zhang, SODA'23] and [Chen, Liu, and Yin, FOCS'23], respectively. Our proof combines ideas from the stochastic dominance argument in the classical censoring inequality and the recently developed high-dimensional expanders. The key step in the proof is a novel comparison result between the Glauber dynamics and the field dynamics for monotone systems.","short_abstract":"We study the mixing time of Glauber dynamics on monotone systems. For monotone systems satisfying the entropic independence condition, we prove a new mixing time comparison result for Glauber dynamics. For concrete applications, we obtain $\\tilde{O}(n)$ mixing time for the random cluster model induced by the ferromagne...","url_abs":"https://arxiv.org/abs/2507.11031","url_pdf":"https://arxiv.org/pdf/2507.11031v1","authors":"[\"Weiming Feng\",\"Minji Yang\"]","published":"2025-07-15T06:51:55Z","proceeding":"cs.DM","tasks":"[\"cs.DM\",\"cs.DS\",\"math-ph\",\"math.PR\"]","methods":"[]","has_code":false}