论文标题
国家驱动的动态图形模型
State-Driven Dynamic Graphon Model
论文作者
论文摘要
本文显示了图形的等效类别的定义阻碍了图形空间上动力学的直接开发，因此提出了一种以状态驱动的方法来获取动态图形。状态驱动的动态图形模型通过分配i.i.d。通用图空间上置换不变概率度量的时间指数序列。状态随机过程到$ \ MathBbm {n} $，而边缘随机变量到每个无序整数对。该模型是从三个角度来证明的：图形限制定义保存，通用性和分析可用性。它通过在通用图空间上的置换不变概率度量和图形子空间中应用置换式概率度量来保留图形的图形限制定义，以获得动态图形，并证明了两者的存在。同样，该模型的广义版本已被证明可以通过著名的Aldous-Hoover表示形式的应用来覆盖Graphon空间，在此，通过在边缘生成功能中添加随机性来实现概括。最后，通过对状态随机过程和边缘随机变量进行假设，对动态图形的行为进行分析可用。
This paper shows the equivalence class definition of graphons hinders a direct development of dynamics on the graphon space, and hence proposes a state-driven approach to obtain dynamic graphons. The state-driven dynamic graphon model constructs a time-index sequence of the permutation-invariant probability measures on the universal graph space by assigning i.i.d. state random processes to $\mathbbm{N}$ and edge random variables to each of the unordered integer pairs. The model is justified from three perspectives: graph limit definition preservation, genericity, and analysis availability. It preserves the graph limit definition of graphon by applying a bijection between the permutation-invariant probability measures on the universal graph space and the graphon space to obtain the dynamic graphon, where the existence of the bijection is proved. Also, a generalized version of the model is proved to cover the graphon space by an application of the celebrated Aldous-Hoover representation, where generalization is achieved by adding randomness to the edge-generating functions. Finally, analysis of the behavior of the dynamic graphon is shown to be available by making assumptions on the state random processes and the edge random variables.
