论文标题
在有限图上流动的动力相变
Dynamical Phase Transitions for Flows on Finite Graphs
论文作者
论文摘要
我们研究了随机在有限的有向图上随机跳跃的粒子模型中的时间平均流。在限制中，随着颗粒数量和时间窗口的数量为无穷大，但图仍然有限，平均流量的大差速器功能由涉及密度和流动路径的变分配方给出。我们提供了足够的条件，在该条件下，给定时间平均流的较大偏差取决于时间恒定的路径。然后，我们考虑在离散环上的一类模型，可以证明可以获得更好的策略，从而产生时间相关的路径。已知这种现象称为动力学相变，在流体动力缩放极限的某些粒子系统中发生，因此将其扩展到有限图的设置。
We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate functional of the average flow is given by a variational formulation involving paths of the density and flow. We give sufficient conditions under which the large deviations of a given time averaged flow is determined by paths that are constant in time. We then consider a class of models on a discrete ring for which it is possible to show that a better strategy is obtained producing a time-dependent path. This phenomenon, called a dynamical phase transition, is known to occur for some particle systems in the hydrodynamic scaling limit, which is thus extended to the setting of a finite graph.
