Large Deviations of the Giant Component in Scale‐Free Inhomogeneous Random Graphs
Abstract
ABSTRACT We study large deviations of the size of the largest connected component in a general class of inhomogeneous random graphs with iid weights, parametrized so that the degree distribution is regularly varying. We derive a large‐deviation principle with logarithmic speed: the rare event that the largest component contains linearly more vertices than expected is caused by the presence of constantly many vertices with linear degree. Conditionally on this rare event, we prove distributional limits of the weight distribution and component‐size distribution.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Complex Network Analysis Techniques
Graph theory and applications
Publication details
- Journal / source
- Random Structures and Algorithms
- Volume
- 68
- Issue
- 4
- Publication date
- 12 June 2026
- Language
- EN