Annealed central limit theorems for the ising model on random graphs
Annealed central limit theorems for the ising model on random graphs
复制标题
随机图上 ising 模型的退火中心极限定理
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
M. L. Prioriello
中科院分区：
文献类型：
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作者：
C. Giardinà;C. Giberti;R. Hofstad;M. L. Prioriello
本文的目的是证明关于退火测度的中心极限定理的磁化重新标度的Ising模型的随机图上的ESN。更准确地说，我们考虑了一般秩为1的非齐次随机图（或广义随机图），2-正则构形模型和度为1和2的构形模型。对于广义随机图，我们首先证明了存在一个有限退火逆临界温度0≤ βan 0和B ≥ 0.在组态模型的情况下，中心极限定理在参数β和B的整个区域都成立，因为这些系统不存在相变，因为它们与一维伊辛模型密切相关。我们的证明是基于显式计算，这是可能的，因为在退火设置的广义随机图上的伊辛模型被减少到一个非齐次居里-外斯模型，而与度只取值1和2的配置模型的分析依赖于经典的一维伊辛模型。
The aim of this paper is to prove central limit theorems with respect to the annealed measure for the magnetization rescaled by √N of Ising models on random graphs. More precisely, we consider the general rank-1 inhomogeneous random graph (or generalized random graph), the 2-regular configuration model and the configuration model with degrees 1 and 2. For the generalized random graph, we first show the existence of a finite annealed inverse critical temperature 0≤ βan n 0 and B ≠ 0. In the case of the configuration model, the central limit theorem holds in the whole region of the parameters β and B, because phase transitions do not exist for these systems as they are closely related to one-dimensional Ising models. Our proofs are based on explicit computations that are possible since the Ising model on the generalized random graph in the annealed setting is reduced to an inhomogeneous Curie-Weiss model, while the analysis of the configuration model with degrees only taking values 1 and 2 relies on that of the classical one-dimensional Ising model.