A short proof of a central limit theorem for the order of the giant component and k‐core
Abstract
Abstract In this note we outline a new and simple approach to proving central limit theorems for various ‘global’ graph parameters that have robust ‘local’ approximations, using the Efron–Stein inequality, which relies on a combinatorial analysis of the stability of these approximations under resampling an edge. As an application, we give short proofs of a central limit theorem for the order of the giant component and of the ‐core for sparse random graphs.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Mathematical Dynamics and Fractals
Geometry and complex manifolds
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 8
- Publication date
- 1 August 2026
- Language
- EN