Degree-Free Spectral Independence for Log-Concave Holant Measures

2026-09-16

AI Summary

本文通过建立度无关的谱独立性界，解决了对数凹Holant问题，并使用Glauber动力学方法为单体-二聚体模型和b-匹配问题提供了松弛时间界限。

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.

Problem

• log-concave
• Holant
• spectral independence
• simple graphs

Innovation

• degree-independent bound
• spectral independence
• log-concave Holant problems
• relaxation-time bounds
• Glauber dynamics