Dynamical Fluctuations of Random Walks in Higher-Order Networks,Physical Review Letters

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Dynamical Fluctuations of Random Walks in Higher-Order Networks
Physical Review Letters ( IF 8.1 ) Pub Date : 2024-09-03 , DOI: 10.1103/physrevlett.133.107401
Leonardo Di Gaetano ₁ , Giorgio Carugno ₂ , Federico Battiston ₁ , Francesco Coghi ₃

Affiliation

Although higher-order interactions are known to affect the typical state of dynamical processes giving rise to new collective behavior, how they drive the emergence of rare events and fluctuations is still an open problem. We investigate how fluctuations of a dynamical quantity of a random walk exploring a higher-order network arise over time. In the quenched case, where the hypergraph structure is fixed, through large deviation theory we show that the appearance of rare events is hampered in nodes with many higher-order interactions, and promoted elsewhere. Dynamical fluctuations are further boosted in an annealed scenario, where both the diffusion process and higher-order interactions evolve in time. Here, extreme fluctuations generated by optimal higher-order configurations can be predicted in the limit of a saddle-point approximation. Our study lays the groundwork for a wide and general theory of fluctuations and rare events in higher-order networks.

Published by the American Physical Society

2024

中文翻译：

高阶网络中随机游走的动态波动

尽管已知高阶交互会影响产生新集体行为的动态过程的典型状态，但它们如何驱动罕见事件和波动的出现仍然是一个悬而未决的问题。我们研究了探索高阶网络的随机游走的动态量的波动是如何随时间产生的。在超图结构固定的淬灭情况下，通过大偏差理论，我们表明罕见事件的出现在具有许多高阶交互的节点中受到阻碍，并在其他地方得到促进。在退火场景中，动力学波动进一步增强，其中扩散过程和高阶相互作用都随时间演变。在这里，可以在鞍点近似的极限内预测最佳高阶配置产生的极端波动。我们的研究为高阶网络中波动和罕见事件的广泛而一般的理论奠定了基础。美国物理学会 2024 年出版

更新日期：2024-09-03

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