论文标题
在Erdös-rényi随机图上的Ising模型的分区函数的波动
Fluctuations for the partition function of Ising models on Erdös-Rényi random graphs
论文作者
论文摘要
我们在Erdős-rényi图上分析了Ising/curie-weiss模型，其中$ n $顶点和边缘概率$ p = p = p（n）$，由Bovier和Gayrard [J. \ Statist。我们证明了模型的分区函数的中心限制定理，并且在其他衰减状态下为$ p（n）$ - 用于对数分区函数。我们发现$ p（n）$的关键制度，分区功能波动的行为发生了变化。
We analyze Ising/Curie-Weiss models on the Erdős-Rényi graph with $N$ vertices and edge probability $p=p(N)$ that were introduced by Bovier and Gayrard [J.\ Statist.\ Phys., 72(3-4):643--664, 1993] and investigated in two previous articles by the authors. We prove Central Limit Theorems for the partition function of the model and -- at other decay regimes of $p(N)$ -- for the logarithmic partition function. We find critical regimes for $p(N)$ at which the behavior of the fluctuations of the partition function changes.
