We study a point process describing the asymptotic behaviour of sizes of the largest components of the random graph G(n,p) in the critical window, that is, for p = n-1 + λn-4/3, where A is a fixed real number. In particular, we show that this point process has a surprising rigidity. Fluctuations in the large values will be balanced by opposite fluctuations in the small values such that the sum of the values larger than a small ε (a scaled version of the number of vertices in components of size greater than εn2/3) is almost constant.
ASJC Scopus subject areas
- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics