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Dynamical Fluctuations of Random Walks in Higher-Order Networks.

Leonardo Di Gaetano¹, Giorgio Carugno², Federico Battiston¹

¹Department of Network and Data Science, <a href="https://ror.org/02zx40v98">Central European University</a>, 1100 Vienna, Austria.

Physical Review Letters

|September 20, 2024

Summary

This summary is machine-generated.

Higher-order interactions influence dynamical processes and rare events in networks. This study reveals how these interactions can either suppress or promote fluctuations, offering insights into network dynamics.

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Area of Science:

Complex Systems
Network Science
Statistical Physics

Background:

Higher-order interactions shape collective behavior in dynamical processes.
The role of these interactions in driving rare events and fluctuations remains largely unexplored.
Understanding fluctuations is crucial for predicting system behavior.

Purpose of the Study:

To investigate the emergence of fluctuations and rare events in random walks on higher-order networks.
To analyze how network structure, specifically higher-order interactions, impacts dynamical fluctuations.
To develop a theoretical framework for fluctuations in higher-order systems.

Main Methods:

Utilizing large deviation theory to analyze quenched (fixed) hypergraph structures.
Employing a saddle-point approximation for annealed (time-evolving) scenarios.
Modeling random walks on higher-order networks.

Main Results:

In quenched networks, nodes with more higher-order interactions suppress rare events, while others promote them.
In annealed networks, dynamical fluctuations are amplified.
Optimal higher-order configurations can predict extreme fluctuations.

Conclusions:

Higher-order interactions play a critical role in modulating rare events and fluctuations.
The study provides a theoretical foundation for understanding dynamics in higher-order networks.
Findings have implications for fields relying on network analysis and dynamical systems.