{"ID":22952730,"CreatedAt":"2026-09-17T02:12:05.498442134Z","UpdatedAt":"2026-09-20T18:11:56.143995915Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.18835","arxiv_id":"2609.18835","title":"Degree-Free Spectral Independence for Log-Concave Holant Measures","abstract":"We establish a degree-independent bound on spectral independence for log-concave Holant problems on simple graphs. As a corollary, we obtain relaxation-time bounds for Glauber dynamics of $O_λ(m)$ for the monomer-dimer model at activity $λ$ and $O_{b,λ}(m)$ for $b$-matchings at fugacity $λ\u003e0$, where $m$ is the number of edges. For uniform $b$-matchings, the relaxation-time bound improves to $O(bm)$. The main proof ideas were found using GPT-5.6 Sol.","short_abstract":"We establish a degree-independent bound on spectral independence for log-concave Holant problems on simple graphs. As a corollary, we obtain relaxation-time bounds for Glauber dynamics of $O_λ(m)$ for the monomer-dimer model at activity $λ$ and $O_{b,λ}(m)$ for $b$-matchings at fugacity $λ\u003e0$, where $m$ is the number o...","url_abs":"https://arxiv.org/abs/2609.18835","url_pdf":"https://arxiv.org/pdf/2609.18835v1","authors":"[\"Xiaoyu Chen\",\"Zejia Chen\",\"Xinyuan Zhang\"]","published":"2026-09-16T15:42:53Z","proceeding":"cs.DS","tasks":"[\"cs.DS\",\"math.PR\"]","methods":"[]","has_code":false}