Title: Limit theorems and lack thereof for a multilayer random walk mimicking human mobility Show Chinese title

Title: 模仿人类流动性的多层随机游动的极限定理及其不足

Abstract: We introduce a continuous-time random walk model on an infinite multilayer structure inspired by transportation networks. Each layer is a copy of $\mathbb{R}^d$, indexed by a non-negative integer. A walker moves within a layer by means of an inertial displacement whose speed is a deterministic function of the layer index and whose direction and duration are random, but with a timescale that depends on the layer. After each inertial displacement, the walker may randomly shift level, up or down, independently of its past. The multilayer structure is hierarchical, in the sense that the speed is a nondecreasing function of the layer index. Our primary focus is on the diffusive properties of the system. Under a natural condition on the parameters of the model, we establish a functional central limit theorem for the $\mathbb{R}^d$-coordinate of the process. By contrast, in a class of examples where this condition is violated, we are able to determine the correct scaling of the process while proving that no limit theorem holds. Show Chinese abstract

Abstract: 我们引入了一个在无限多层结构上的连续时间随机游走模型，该结构受交通网络的启发。每一层都是一个拷贝$\mathbb{R}^d$，由一个非负整数索引。行走者通过惯性位移在一个层内移动，其速度是层索引的确定性函数，其方向和持续时间是随机的，但有一个与层相关的时标。每次惯性位移后，行走者可能随机地向上或向下切换层，与其过去无关。多层结构是分层的，即速度是层索引的非减函数。我们的主要关注点是系统的扩散性质。在模型参数的一个自然条件下，我们建立了过程的$\mathbb{R}^d$坐标的泛函中心极限定理。相比之下，在一类违反此条件的例子中，我们能够确定过程的正确尺度，同时证明没有极限定理成立。