论文标题
空腔主方程：在随机图中的铁磁模型的平均值和固定点
The Cavity Master Equation: average and fixed point of the ferromagnetic model in random graphs
论文作者
论文摘要
空腔主方程（CME）是代表连续时间离散变量动力学的常用主方程的封闭方案。在这项工作中，我们探索了随机图中铁磁模型的CME。我们首先得出CME的平均方程，描述了系统平均磁化的动力学。我们表明，数值结果与蒙特卡洛模拟相比之下。然后，我们表明，CME的固定状态由BP样方程（独立于使系统朝向固定态的动态规则）进行很好的描述。如果人们还假设固定状态通过玻尔兹曼分布很好地描述，则可以将这些方程式重写为腔方程的固定点解。
The Cavity Master Equation (CME) is a closure scheme to the usual Master Equation representing the dynamics of discrete variables in continuous time. In this work we explore the CME for a ferromagnetic model in a random graph. We first derive and average equation of the CME that describes the dynamics of mean magnetization of the system. We show that the numerical results compare remarkably well with the Monte Carlo simulations. Then, we show that the stationary state of the CME is well described by BP-like equations (independently of the dynamic rules that let the system towards the stationary state). These equations may be rewritten exactly as the fixed point solutions of the Cavity Equation if one also assumes that the stationary state is well described by a Boltzmann distribution.
