论文标题
随机步行在图上的离域化 - 定位动力学相变
Delocalization-localization dynamical phase transition of random walks on graphs
论文作者
论文摘要
我们考虑在两个连接和无向图的模型上随机步行，并研究可观察到的局部动力学的确切大偏差。我们证明，在热力学极限中，这种可观察到的可观察到的是一阶动力相变（DPT）。这被解释为访问图形高度连接的大部分图（定位）和访问边界的路径的波动中路径的“共存”。我们使用的方法还允许我们通过分析表征缩放函数，描述了局部化和离域机制之间的有限大小交叉。值得注意的是，我们还表明，DPT在图形拓扑的变化方面是强大的，这仅在交叉状态中起作用。所有结果都支持这样的观点，即一阶DPT也可能出现在无限大小随机图上的随机步行中。
We consider random walks evolving on two models of connected and undirected graphs and study the exact large deviations of a local dynamical observable. We prove, in the thermodynamic limit, that this observable undergoes a first-order dynamical phase transition (DPT). This is interpreted as a `co-existence' of paths in the fluctuations that visit the highly connected bulk of the graph (delocalization) and paths that visit the boundary (localization). The methods we used also allow us to characterize analytically the scaling function that describes the finite size crossover between the localized and delocalized regimes. Remarkably, we also show that the DPT is robust with respect to a change in the graph topology, which only plays a role in the crossover regime. All results support the view that a first-order DPT may also appear in random walks on infinite-size random graphs.
