复杂网络上的恢复随机游走与极端事件
Recovery Random Walks and Extreme Events on Complex Networks
- Indian Institute of Science Education and Research Thiruvananthapuram（印度科学教育研究所特里凡得琅分校）
- SASTRA Deemed University（萨斯特拉大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出恢复随机游走模型，通过冻结极端事件节点抑制其概率与频率，并给出解析预测，更贴近现实。
AI中文摘要：
极端事件在简单随机游走框架内被广泛研究，其概率由网络结构和稳态游走者分布决定。在此，我们提出一种恢复随机游走（RRW）模型，其中极端事件会暂时“冻结”其发生的节点，持续固定时间Δ（Δ=0时恢复原始模型），从而困住游走者并减少有效移动群体，使模型更具实用性。我们推导了这种反馈的第一性原理描述，以及冻结节点比例的延迟微分方程。这种有限冻结产生初始过冲，随后以阻尼振荡方式弛豫至冻结节点比例的稳态。我们发现，冻结抑制了极端事件概率，同时保留其度依赖动态，并抑制极端事件频率。此外，冻结节点比例的解析预测与模拟结果高度吻合。该模型紧密反映现实场景，产生更实用的极端事件统计。
英文摘要：
Extreme events are widely studied within simple random walk frameworks, where their probability is determined by the network structure and stationary walker distribution. Here, we propose a recovery random walk (RRW) model in which extreme events temporally `freeze' the nodes where they occur for a fixed duration $Δ$ ($Δ=0$ recovers the original model), trapping walkers and reducing the effective mobile population, thereby making the model more practical. We derive a first-principles description of this feedback and a delayed differential equation for the frozen-node fraction. This finite freezing produces an initial overshoot, followed by damped oscillatory relaxation to a steady state for the fraction of the frozen nodes. We find that freezing suppresses extreme event probability while preserving its degree dependence dynamics, and suppresses the EE frequency. Further, the analytical prediction for the fraction of the frozen nodes agrees closely with simulations. This model closely reflects real-world scenarios, yielding more practical EE statistics.
