发表机构
University of Minnesota; National Taiwan University（明尼苏达大学; 台湾大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了具有给定度数的随机图（包括d-正则图）上最大权匹配权重的退火中心极限定理，通过分离边权重与图的波动，并利用更强的微扰相关性衰减估计和方差界，归结为配置模型局部统计量的中心极限定理。
AI 中文摘要
我们证明了在具有给定且一致有界度数的均匀随机简单图上，最大权匹配的权重的退火中心极限定理，其中边权重为独立同分布的指数分布。特别地，该结果适用于每个固定 $d \ge 2$ 的随机 $d$-正则图。证明将来自边权重的波动与来自图的波动分开。Lam 和 Sen ( arXiv:2511.18861 ) 的相关性衰减估计给出了前者的高斯波动。主要困难在于分析给定图时最优权重的条件均值的波动。为了解决这个问题，我们证明了一个更强的微扰相关性衰减估计，该估计与一个方差界一起，将问题归结为 Barbour 和 Röllin [Ann. Appl. Probab. 29(2) (2019)] 关于配置模型的局部统计量的中心极限定理。
英文摘要
We prove an annealed central limit theorem for the weight of the maximum weight matching on uniformly random simple graphs with prescribed, uniformly bounded degrees and i.i.d. exponential edge weights. In particular, the result applies to random $d$-regular graphs for every fixed $d \ge 2$. The proof separates the fluctuations arising from the edge weights from those arising from the graph. The correlation decay estimate of Lam and Sen (arXiv:2511.18861) yields Gaussian fluctuations for the former. The main difficulty is to analyze the fluctuations of the conditional mean of the optimal weight given the graph. To address this, we prove a stronger perturbative correlation decay estimate that, together with a variance bound, reduces the problem to the central limit theorem of Barbour and Röllin [Ann. Appl. Probab. 29(2) (2019)] for local statistics of the configuration model.
Comments46 pages, 4 figures
