Rare events and discontinuous percolation transitions

Area of Science:

• Network science
• Statistical physics
• Complex systems

Background:

• Percolation theory models network robustness against random node damage.
• Real-world finite networks exhibit fluctuations beyond average behavior.
• Assessing collapse risk from rare damage configurations is crucial.

Purpose of the Study:

• Develop a large deviation theory for percolation in sparse networks.
• Characterize network response to rare damage events.
• Analyze phase transitions under extreme conditions.

Main Methods:

• Formulated a large deviation theory for percolation.
• Analyzed the behavior of sparse networks under rare events.
• Investigated phase transitions beyond average network response.

Main Results:

• The theory encompasses standard second-order phase transitions.
• Identified discontinuous transitions for rare damage configurations.
• Demonstrated suppression of the giant component size in specific rare events.

Conclusions:

• Large deviation theory provides a more complete understanding of network robustness.
• Finite networks face unique collapse risks due to rare events.
• The findings have implications for network resilience in biology, epidemics, and infrastructure.