记忆对网络上随机游动动力学的影响
Effect of Memory on the Dynamics of Random Walks on Networks
摘要：
在现实世界的系统中观察到的扩散路径往往需要超越一阶马尔可夫模型的随机过程，如网络理论中隐含的假设。在这项工作中，我们专注于二阶马尔可夫模型，并推导出一个解析表达式的记忆的影响的谱间隙，从而等价地，随机过程渐近达到平衡所需的特征时间。扰动分析表明，标准的一阶马尔可夫模型可以高估或低估的扩散率的流量通过模块化结构的系统捕获的二阶马尔可夫网络。我们测试的玩具的例子和数值数据的理论预测，并讨论其对网络理论的影响，特别是在时间或多重网络的情况下。
英文摘要：
Pathways of diffusion observed in real-world systems often require stochastic processes going beyond first-order Markov models, as implicitly assumed in network theory. In this work, we focus on second-order Markov models, and derive an analytical expression for the effect of memory on the spectral gap and thus, equivalently, on the characteristic time needed for the stochastic process to asymptotically reach equilibrium. Perturbation analysis shows that standard first-order Markov models can either overestimate or underestimate the diffusion rate of flows across the modular structure of a system captured by a second-order Markov network. We test the theoretical predictions on a toy example and on numerical data, and discuss their implications for network theory, in particular in the case of temporal or multiplex networks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
