论文标题
随机图上相互作用动力学系统的大偏差原理
The large deviation principle for interacting dynamical systems on random graphs
论文作者
论文摘要
使用针对大偏差的弱收敛方法，我们在切割拓扑中制定并证明了W-random图的大偏差原理（LDP）。这概括了Chatterjee和Varadhan的Erdős-r {\'e} NYI随机图的LDP。此外，我们将随机图的LDP转换为此类图上的一类交互动力系统。为此，我们证明了动力学模型的解决方案在相对于切口和应用收缩原理方面连续取决于基础图。
Using the weak convergence approach to large deviations, we formulate and prove the large deviation principle (LDP) for W-random graphs in the cut-norm topology. This generalizes the LDP for Erdős-R{\' e}nyi random graphs by Chatterjee and Varadhan. Furthermore, we translate the LDP for random graphs to a class of interacting dynamical systems on such graphs. To this end, we demonstrate that the solutions of the dynamical models depend continuously on the underlying graphs with respect to the cut-norm and apply the contraction principle.
