论文标题
无序单体二聚体模型中的中心极限定理
Central Limit Theorem in Disordered Monomer-Dimer Model
论文作者
论文摘要
我们考虑具有有界度的一般有限图上的无序单体二聚体模型。在重量分布的有限第四矩假设下，我们证明了相关吉布斯的自由能测量的高斯中心极限定理，并以收敛速率测量。如果在几乎最佳的有限$（2+ε）$ - 时刻假设下，则中央限制定理继续保持权重分布，如果基础图进一步假定具有均匀的亚指数体积增长。这概括了Dey和Krishnan（Arxiv：2109.12716）的最新结果，他们在圆柱图上显示了无序的单体二聚体模型中的高斯中心极限定理。我们的证明依赖于无序单体二聚体模型表现出与高概率相关的衰减的想法。我们还为基础图具有亚指数体积生长的二聚体数量的Gibb的平均值建立了一个中心极限定理，而边缘权重为高斯。
We consider the disordered monomer-dimer model on general finite graphs with bounded degrees. Under the finite fourth moment assumption on the weight distributions, we prove a Gaussian central limit theorem for the free energy of the associated Gibbs measure with a rate of convergence. The central limit theorem continues to hold under a nearly optimal finite $(2+ε)$-moment assumption on the weight distributions if the underlying graphs are further assumed to have a uniformly subexponential volume growth. This generalizes a recent result by Dey and Krishnan (arXiv:2109.12716) who showed a Gaussian central limit theorem in the disordered monomer-dimer model on cylinder graphs. Our proof relies on the idea that the disordered monomer-dimer model exhibits a decay of correlation with high probability. We also establish a central limit theorem for the Gibbs average of the number of dimers where the underlying graph has subexponential volume growth and the edge weights are Gaussians.
