Dynamical fluctuations of random walks in higher-order networks

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 expl...

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Bibliographic Details
Published in:arXiv.org 2024-07
Main Authors: Leonardo Di Gaetano, Carugno, Giorgio, Battiston, Federico, Coghi, Francesco
Format: Article
Language:English
Subjects:
Phase transitions
Random walk
Online Access:Get full text
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Summary: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. \newtext{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.
ISSN:2331-8422