AI 中文总结
该研究提出了单纯复形上基于关联关系的随机游走模型，发现部分面保留产生的异质高阶连通性会在中间面密度处形成传输瓶颈，相关谱与传输特性呈非单调变化，为研究高阶连通性对网络性质的影响提供了框架。
AI 中文摘要
我们在具有完全1-骨架且独立保留三角形面的随机二维单纯复形的边上引入一种基于关联关系的随机游走。该动力学结合了两种传输通道，一种由顶点介导，另一种由三角形面介导，通过混合参数q控制的有效转移算子实现。这种构造在不改变游走底层成对支撑的情况下，分离了高阶连通性的影响。我们通过结构可观测量、谱弛豫、平稳局域化和首通传输对该模型进行表征。结果表明，部分面保留会产生异质高阶连通性，在中间面密度处产生明显的传输瓶颈。在该区域，第二大特征值模、平稳分布的逆参与率以及平均首通时间均表现出非单调行为，在中间面密度处达到最大值。相应的首通时间分布显示出异常长轨迹的概率增加。这些结果共同建立了一个简单框架，用于研究异质高阶连通性如何重塑超出成对网络动力学的谱和传输性质。
英文摘要
We introduce an incidence-based random walk on the edges of a random two-dimensional simplicial complex with a complete $1$-skeleton and independently retained triangular faces. The dynamics combine two transport channels, one mediated by vertices and the other by triangular faces, through an effective transition operator controlled by a mixing parameter $q$. This construction isolates the effects of higher-order connectivity without modifying the underlying pairwise support of the walk. We characterize the model through structural observables, spectral relaxation, stationary localization, and first-passage transport. Our results show that partial face retention generates heterogeneous higher-order connectivity, giving rise to a pronounced transport bottleneck at intermediate face densities. In this regime, the second-largest eigenvalue modulus, the inverse participation ratio of the stationary distribution, and the mean first-passage time all exhibit non-monotonic behavior, reaching their largest values at intermediate face densities. The corresponding first-passage-time distributions reveal an enhanced probability of unusually long trajectories. Together, these results establish a simple framework for investigating how heterogeneous higher-order connectivity reshapes spectral and transport properties beyond pairwise network dynamics.
