Year: 2026
Type: preprint
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 $λ>0$, 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.
Source: arXiv (Cornell University)
Authors: Chen, Xiaoyu, Chen, Zejia, Zhang, Xinyuan
Institution: Massachusetts Institute of Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213499490