随机图中无序系统随机动力学的从随机点过程到分层腔主方程：伊辛模型和流行病
From random point processes to hierarchical Cavity Master Equations for the stochastic dynamics of disordered systems in Random Graphs: Ising models and epidemics
摘要：
我们从随机点过程理论出发，导出了描述随机图中离散变量连续动力学的n点耦合主方程。这些方程构成了一个层次的近似，推广和改进腔主方程（CME）最近在其他出版物中获得。我们的推导澄清了最初导致CME的一些假设和近似，现在被认为是一个更一般的技术的第一顺序。我们测试了新的计划在稀释图定义的三个模型的动力学：伊辛铁磁体，维亚纳-布雷自旋玻璃和传染病易感模型的流行病。在前两种情况下，新方程的性能与文献中最知名的方法相似。在后者，他们优于著名的对淬火平均场近似。
英文摘要：
We start from the Theory of Random Point Processes to derive n-point coupled master equations describing the continuous dynamics of discrete variables in random graphs. These equations constitute a hierarchical set of approximations that generalize and improve the Cavity Master Equation (CME) recently obtained in other publications. Our derivation clarifies some of the hypotheses and approximations that originally lead to the CME, considered now as the first order of a more general technique. We tested the new scheme in the dynamics of three models defined over diluted graphs: the Ising ferromagnet, the Viana-Bray spin-glass and the susceptible-infectious-susceptible model for epidemics. In the first two, the new equations perform similarly to the best-known approaches in the literature. In the latter, they outperform the well-known Pair Quenched Mean-Field Approximation.
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