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Area of Science:

  • Probability theory
  • Statistical physics
  • Network science

Background:

  • Bootstrap percolation models infection spread on graphs.
  • Erdős-Rényi random graphs are a fundamental model for network structure.
  • Previous work established critical conditions for widespread infection.

Purpose of the Study:

  • Investigate atypical, large-deviation events in bootstrap percolation.
  • Quantify the probability of unexpected infection spread from small initial sets.
  • Identify the most efficient pathways for such large deviations.

Main Methods:

  • Analysis of bootstrap percolation dynamics on Erdős-Rényi random graphs.
  • Large deviation theory to calculate rate functions.
  • Identification of minimum-cost trajectories for rare events.

Main Results:

  • Calculated the rate function for small initial sets causing unexpected large infections.
  • Identified the least-cost trajectory for realizing these large deviations.
  • Characterized the probability of rare, extensive infection spread.

Conclusions:

  • Provides a deeper understanding of extreme events in random network percolation.
  • Offers insights into the dynamics of rare but significant spread phenomena.
  • Contributes to the statistical analysis of complex systems.